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Coordinate Geometry

Description: Coordinate Geometry
Number of Questions: 40
Created by:
Tags: Coordinate Geometry Plotting of Points Plotting Points Identification of Quadrants Co-Ordinate Geometry
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On which axis does the point (-7, 0) lie?

  1. Positive x–axis

  2. Positive y–axis

  3. Negative x–axis

  4. Negative y–axis


Correct Option: C
Explanation:

As (–7, 0) $\leftrightarrow $ (x, y), where x coordinate is -7, i.e. negative and y coordinate is 0, so the point (–7, 0) lies on the negative x-axis.

The horizontal axis in the Cartesian plane is the

  1. z–axis

  2. x–axis

  3. y–axis

  4. w–axis


Correct Option: B
Explanation:

In the Cartesian plane, the x-axis is the horizontal axis.

On which axis does the point (- 5, 0) lie?

  1. Negative x–axis

  2. Positive y–axis

  3. Positive x–axis

  4. Negative y–axis


Correct Option: A
Explanation:

Point (- 5, 0) corresponds to (x, y). Here, x-coordinate is - 5, i.e. negative and y-coordinate is 0. $\Rightarrow$So, the point (- 5, 0) lies on the negative x-axis.

The vertical axis in the Cartesian plane is ______.

  1. y-axis

  2. x-axis

  3. z-axis

  4. none of these


Correct Option: A
Explanation:

The vertical (standing) axis of a Cartesian plane is y-axis.

The horizontal and vertical axis drawn on the plane divides the whole plane into _______.

  1. quadratics

  2. quarks

  3. quadrates

  4. quadrants


Correct Option: D
Explanation:

The horizontal and vertical axis drawn on the plane divides the whole plane into quadrants.

In which of the following quadrants does the point (–5, –4) lie?

  1. I

  2. II

  3. III

  4. IV


Correct Option: C
Explanation:

(–5, –4) $\Rightarrow$ Both x and y coordinates are negative. When x < 0 and y < 0, the point lies in the third quadrant. So, the point (5, 4) lies in the third quadrant. 

On which axis does the point $\biggl(- \frac{2}{3}, 0\biggr)$lie?

  1. Negative x–axis

  2. Positive y–axis

  3. Positive x–axis

  4. Negative y–axis


Correct Option: A
Explanation:

As the point $\biggl(- \frac{2}{3}, 0\biggr) \leftrightarrow (x,y) $ Here, x co-ordinate is $\frac{-2}{3}$, which is negative and y co-ordinate is 0. So, the point $\biggl(- \frac{2}{3}, 0\biggr)$lies on the negative x-axis.

What do we call the point where the horizontal and the vertical axis meet in the Cartesian plane?

  1. Origin

  2. Orient

  3. Original

  4. Originate


Correct Option: A
Explanation:

The meeting point of two axes in the Cartesian plane is called origin (0, 0).

In which of the following quadrants does the point $\biggl(\frac{4}{5}, -2 \biggr)$lie?

  1. IV

  2. I

  3. II

  4. III


Correct Option: A
Explanation:

The point is $\biggl(\frac{4}{5}, -2 \biggr)$. It corresponds to (x, y). When x > 0 and y < 0, the point lies in the 4th quadrant. So, the point $\biggl( \frac{4}{5}, -2 \biggr)$ lies in the 4th quadrant.

On which axis does the point (0, – 11) lie?

  1. Negative x–axis

  2. Negative y–axis

  3. Positive x–axis

  4. Positive y–axis


Correct Option: B
Explanation:

The point is (0, – 11) $\leftrightarrow $ (x, y) Here, x-coordinate is 0 and y-coordinate is – 11. So, the point lies on the negative y-axis.

The perpendicular distance of the point (6, – 5) from the x–axis is _______.

  1. – 5 units

  2. 5 units

  3. 6 units

  4. – 6 units


Correct Option: B
Explanation:

The perpendicular distance of the point (6, – 5) from the x-axis will be y-coordinate but with a positive sign as distance is never negative. So, the perpendicular distance of (6, – 5) from the x-axis is 5 units.

On which axis does the point (0, 3) lie?

  1. Positive x–axis

  2. Positive y–axis

  3. Negative y–axis

  4. Negative x–axis


Correct Option: B
Explanation:

The point (0, 3) $\leftrightarrow $ (x, y) Here, the x-coordinate is 0 and the y-coordinate is 3. $\therefore$ The point (0, 3) lies on the positive y-axis.

If (a, b) be any point in the Cartesian plane, then 'b' is called ______.

  1. abscissa

  2. x-axis

  3. ordinate

  4. y-axis


Correct Option: C
Explanation:

The y co-ordinate is also known as ordinate and b is the y co-ordinate of point (a, b). So, 'b' is called ordinate.

In which of the following quadrants does the point (17, 9) lie?

  1. 1st quadrant

  2. 2nd quadrant

  3. 3rd quadrant

  4. 4th quadrant


Correct Option: A
Explanation:

The point is (17, 9) $\leftrightarrow $ (x, y) Here, x > 0 and y > 0 and if x is positive and y is positive, then the point lies in the 1st quadrant. So, point (17, 9) lies in the first quadrant.                                                 OR The sign of co-ordinate of a point is (+, +), which lies in 1st quadrant. So, (17, 9) lies in the first quadrant.

On which axis does the point (8, 0) lie?

  1. Negative y–axis

  2. Positive y–axis

  3. Positive x–axis

  4. Negative x–axis


Correct Option: C
Explanation:

As the point is (8, 0)         (8, 0) $\leftrightarrow $ (x, y) Here, x-coordinate is 8 which is greater than 0 and y-coordinate is 0, and when y-coordinate is 0, then the point lies on xaxis. As the x-coordinate is greater than 0, the point (8, 0) lies on positive xaxis.

The perpendicular distance of point (– 7, 9) from the y–axis is ______.

  1. – 7 units

  2. 7 units

  3. 9 units

  4. – 9 units


Correct Option: B
Explanation:

The perpendicular distance from yaxis of any point is x co-ordinate but distance is always positive. So, the perpendicular distance of (– 7, 9) from yaxis is 7 units.

In which of the following quadrants does the point (11, – 15) lie?

  1. 1st quadrant

  2. 2nd quadrant

  3. 3rd quadrant

  4. 4th quadrant


Correct Option: D
Explanation:

The point is (11, – 15). Here, x-coordinate is 11 > 0 and y-coordinate is – 15 < 0, and the signs of the coordinates are (+, –), which lie in the 4th quadrant. So, the point (11, – 15) lies in the 4th quadrant.

On which axis does the point (0, 6) lie?

  1. Negative x–axis

  2. Negative y–axis

  3. Positive x–axis

  4. Positive y–axis


Correct Option: D
Explanation:

When x-coordinate is 0, the point lies on the y–axis. $\therefore$ The point (0, 6) lies on the positive yaxis.

The perpendicular distance of (13, 12) from the y–axis is ______.

  1. 13 units

  2. – 13 units

  3. 12 units

  4. – 12 units


Correct Option: A
Explanation:

The perpendicular distance from yaxis of any point is x co-ordinate but distance can never be negative. So, the perpendicular distance of (13, 12) from yaxis is 13.

In which of the following quadrants does the point (– 7, 6) lie?

  1. 1st quadrant

  2. 2nd quadrant

  3. 3rd quadrant

  4. 4th quadrant


Correct Option: B
Explanation:

The point is (– 7, 6). Here, x co-ordinate is – 7 < 0 and y co-ordinate is 6 > 0 i.e. x < 0 and y > 0, and when x is negative and y is positive, then the point lies in 2nd quadrant. So, the point (– 7, 6) lies in the 2nd quadrant.

On which axis does the point (7, 0) lie?

  1. Negative y–axis

  2. Positive y–axis

  3. Positive x–axis

  4. Negative x–axis


Correct Option: C
Explanation:

As the point is (7, 0),         (7, 0) $\leftrightarrow $ (x, y) Here, x co-ordinate is 7 which is positive and y co-ordinate is 0, and when y co-ordinate is 0, then the point lies on xaxis. So, the point (7, 0) lies on positive xaxis.

In which of the following quadrants does the point $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$lie?

  1. 3rd quadrant

  2. 1st quadrant

  3. 2nd quadrant

  4. 4th quadrant


Correct Option: A
Explanation:

The point is $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$. Here, x-coordinate is $\frac{-8}{6}$, which is negative, and y-coordinate is $\frac{-7}{3}$, which is also negative. i.e. x < 0 and y < 0 When x < 0 and y < 0, the point lies in the third quadrant. So, the point $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$ lies in the third quadrant.

The perpendicular distance of (- 2, - 4) from the x-axis is ______.

    • 4 units
    • 2 units
  1. 2 units

  2. 4 units


Correct Option: D
Explanation:

The perpendicular distance of a point (- 2, - 4) from x-axis will be y co-ordinate but with a positive sign, as the distance is never negative. So, the perpendicular distance of (- 2, - 4) from x-axis is 4 units.

On which axis does the point (0, – 3) lie?

  1. Negative x–axis

  2. Negative y–axis

  3. Positive y–axis

  4. Positive x–axis


Correct Option: B
Explanation:

The point is (0, – 3). Here, y co-ordinate is – 3, which is negative and when x co-ordinate is zero, then the point lies on y-axis. So, the point (0, – 3) lies on the negative y-axis.

In which of the following quadrants does the point (– 2, 5) lie?

  1. 4th quadrant

  2. 2nd quadrant

  3. 1st quadrant

  4. 3rd quadrant


Correct Option: B
Explanation:

The point is (– 2, 5). Here, x-co-ordinate is – 2 < 0 and y co-ordinate is 5 > 0. And when x < 0 and y > 0 in the point (x, y), then the point lies in the second quadrant. So, the point (– 2, 5) lies in the 2nd quadrant.                                                             OR The signs of the co-ordinates of point are (–, +), which lies in the 2nd quadrant. So, the point (– 2, 5) lies in the 2nd quadrant.

The perpendicular distance of (11, –9) from the x–axis is

  1. 11 units

  2. –11 units

  3. 9 units

  4. –9 units


Correct Option: C
Explanation:

The perpendicular distance of the point (11, –9) from the x-axis will be y coordinate of the point, but with a positive sign as the distance is never negative. So, the perpendicular distance of (11, –9) from the x-axis is 9 units.

In which of the following quadrants does the point (7, 3) lie?

  1. 2nd quadrant

  2. 3rd quadrant

  3. 1st quadrant

  4. 4th quadrant


Correct Option: C
Explanation:

The point is (7, 3) $\leftrightarrow $ (x, y) Here, x > 0 and y > 0, and when x > 0 and y > 0, the point (x, y) lies in the first quadrant. Then, the point (7, 3) lies in the 1st quadrant.

On which axis does the point (6, 0) lie?

  1. Negative y-axis

  2. Negative x-axis

  3. Positive y-axis

  4. Positive x-axis


Correct Option: D
Explanation:

As the point is (6, 0),             (6, 0) $\leftrightarrow $ (x, y) Here, x co-ordinate is 6, which is positive and y co-ordinate is 0. When y co-ordinate of a point is 0, then the point lies on x-axis. So, the point (6, 0) lies on positive x-axis.

In which of the following quadrants does the point (4, – 8) lie?

  1. 2nd quadrant

  2. 3rd quadrant

  3. 1st quadrant

  4. 4th quadrant


Correct Option: D
Explanation:

The point is (4, – 8). Here, x co-ordinate is 4 > 0 and y co-ordinate is – 8 < 0. When x > 0 and y < 0, then the point (x, y) lies in the 4th quadrant. So, the point (4, – 8) lies in the fourth quadrant.                                                 OR The signs of co-ordinates of point are (+, –), which lies in the 4th quadrant. So, the point (4, – 8) lies in the 4th quadrant.

In which of the following quadrants does the point (– 7, – 9) lie?

  1. 1st quadrant

  2. 2nd quadrant

  3. 3rd quadrant

  4. 4th quadrant


Correct Option: C
Explanation:

The point is (– 7, – 9). Here, x co-ordinate is – 7, which is negative and y co-ordinate is – 9, which is also negative. When x < 0 and y < 0, then the point (x, y) lies in the third quadrant. So, the point (– 7, – 9) lies in the third quadrant.                                                 OR The signs of co-ordinates of the point are (–, –), which lies in the 3rd quadrant. So, the point (– 7, – 9) lies in the third quadrant.

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point D?

  1. (11, –6)

  2. (–6, 11)

  3. (11, 6)

  4. (–11, 6)


Correct Option: A
Explanation:

Since ordered pair is written in the order (x, y), where x = x coordinate of that point and y = y coordinate of that point, so the ordered pair for point D is (11, –6). 

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point E?

  1. (11, – 3)

  2. (3, 11)

  3. (– 11, – 3)

  4. (11, 3)


Correct Option: D
Explanation:

Because ordered pair representing any point is written as (x, y), where x = x-coordinate of that point and y = y-coordinate of that point. $\therefore$    The ordered pair representing the point E is (11, 3).

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point B?

  1. (3, 0)

  2. (0, 3)

  3. (– 3, 0)

  4. (0, – 3)


Correct Option: B
Explanation:

The point B lies on y-axis; so the x-coordinate must be zero and y-coordinate must be 3. Thus, the ordered pair representing the point B is (0, 3).

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point A?

  1. (–8, –7)

  2. (7, –8)

  3. (8, –7)

  4. (–8, 7)


Correct Option: D
Explanation:

 (–8, 7) represents point A on the graph.

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point C?

  1. (10, 8)

  2. (– 10, – 8)

  3. (– 8, – 10)

  4. (8, 10)


Correct Option: B
Explanation:

The ordered pair representing C is (– 10, – 8) as the ordered pairs are written in the order (x, y), where x = x-coordinate of the point and y = y-coordinate of the point.

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point H?

  1. (– 12, 5)

  2. (5, – 12)

  3. (5, 12)

  4. (– 5, 12)


Correct Option: B
Explanation:

The ordered pair representing point H is (5, – 12) as ordered pairs are written in the order (x, y), where x = x-coordinate of the point and y = y-coordinate of the point.

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point I?

  1. (3, 13)

  2. (13, 3)

  3. (– 3, – 13)

  4. (– 3, 13)


Correct Option: A
Explanation:

As the ordered pair representing a point is written as (x, y), where x = x-coordinate of the point and y = y-coordinate of the point. Then, the ordered pair representing I is (3, 13).

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point F?

  1. (10, - 6)

  2. (6, - 10)

  3. (- 6, 10)

  4. (6, 10)


Correct Option: C
Explanation:

As the ordered pair for any point is written in the form (x, y), where x = x co-ordinate of the point and y = y co-ordinate of the point. Then, the ordered pair representing F is given by (- 6, 10).

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point J?

  1. (6, 6)

  2. (6, - 6)

  3. (- 6, 6)

  4. (- 6, - 6)


Correct Option: A
Explanation:

As the ordered pair representing any point is given by (x, y), where x = x co-ordinate of the point and y = y co-ordinate of the point. Then, the ordered pair representing J is given by (6, 6).

Directions: Study the given graph and answer the question.

Which of the following ordered pairs represents the point G?

  1. (- 10, - 5)

  2. (- 5, - 10)

  3. (5, 10)

  4. (5, - 10)


Correct Option: B
Explanation:

As the ordered pair representing any point is given by (x, y), where x = x co-ordinate of that point and y = y co-ordinate of that point. Then, the ordered pair representing G is given by (- 5, - 10).

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