Midpoints - class-XI
Description: midpoints | |
Number of Questions: 102 | |
Created by: Shiva Nambiar | |
Tags: straight lines section and mid-point formula coordinate geometry constructions geometry and algebra straight lines and quadratic equations prerequisites co-ordinate geometry lines maths |
If $O(0,4)$ and $P(0,-4)$, are the co-ordinates of the line segment $OP$ then co-ordinate of its midpoint are
Find the mid point of $(9,5)$ and $(3,7)$
The mid point of $(8,3)$ and $(4,9)$ is
The mid point of $(-1,-3)$ and $(3,7)$
The mid point of $(4,9) $ and $(8,3)$ is
The mid point of $(2,3)$ and $(8,9)$ is
The mid point of $(3,4)$ and $(1,-2)$
The mid-point of the line segment joining $( 2a, 4)$ and $(-2, 2b)$ is $(1, 2a + 1 )$. The values of $a$ and $b$ are
The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is
If Q$\displaystyle \left ( \frac{a}{3},4 \right )$ is the mid-point of the line segment joining the points A(-6,5) and B(-2,3), then the value of 'a' is
A triangle has vertices A(1,-1) B(2,4) and C(6,0) The length of the median from A is
The midpoint of the line segment between P$\displaystyle _{1}$ (x, y) and P$\displaystyle _{2}$ (-2, 4) is P$\displaystyle _{m}$ (2, -1). Find the coordinate.
If (-2, -4) is the midpoint of (6, -7) and (x, y) then the values of x and y are
In the xy-plane, find the mid point of the line segment joining the points $\left( 5,9 \right) $ and $\left( 7,11 \right) $.
The coordinates of points $P(-2, 2), Q(3, 2) $ and $R(3, -2)$ are the vertices of a rectangle $PQRS$`. What are the coordinates of S?
$M$ is the midpoint of the straight line $PQ$. If $P(-2,9)$ and $M$ is $(4,3)$, find the coordinates of $Q$.
$M(2, 6)$ is the midpoint of $\overline {AB}$. If $A$ has coordinates $(10, 12)$, the coordinates of $B$ are
If the mid-point between the points $(a+ b, a- b)$ and $(-a, b)$ lies on the line $ax + by = k$, what is k equal to?
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
If $O(0,0)$ and $P(-8,0)$ then co-ordinates of its midpoint are________.
The mid point of line $AB$ with $A(2,3)$ and $B(5,6)$
$(5,-2)$ is the middle line segment joining the parts $\left(\dfrac {x}{2},\dfrac {y+1}{2}\right)$ and $(x+1,y-3)$ then find the value of $x$ & $y$.
Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are $(0.-1), (2, 1) and (0, 3)$
What is the y intercept of the line that is parallel to $y=3x,$ and which bisects the area of rectangle with corners at $(0,0), (4,0) ,(4,2) $ and $(0,2)$?
The mid-point of the line $(a, 2)$ and $(3, 6)$ is $(2, b)$. Find the numerical values of $a$ and $b$.
If $(3, -4)$ and $(-6, 5)$ are the extremities of a diagonal of a parallelogram and $(2, 1)$ is its third vertex, then its fourth vertex is?
If $(6, -3)$ is the one extremity of diameter to the circle $x^{2}+y^{2}-3x+8y-4=0$ then its other extremity is-
The length of the median from the vertex A of a triangle whose vertices are $A (-1, 3),$ B $(1, -1)$ and C$(5,1)$ is
The locus of mid points of chords to the circle $x^{2}+y^{2}-8x+6y+20=0$ which are parallel to the line $3x+4y+5=0$
If $(2, 3), (-4, 5), (1, -2)$ are the midpoints of the sides $\vec{BC}, \vec{CA}, \vec{AB}$ of $\triangle ABC$, then the equation of $\vec{AB}$ is
The point on $X-axis$ equidistant from $(2,3)$and $(1,5)$ is
Let ${P} _{1}$ and ${P} _{2}$ be two fixed points in $xy-plane$. A line ${L} _{1}=0$ passes through ${P} _{1}$ intersects $y-axis$ at $B$ and the line ${L} _{2}=0$ passes through ${P} _{2}$ and intersects $x-axis$ at $A$. If ${L} _{1}=0$ and ${L} _{2}=0$ are perpendicular then the locus of mid-point of$AB$ is
The point which is equidistant from the points $(-1,1,3),(2,1,2),(0,5,6)$ and $(3,2,2)$ is
The point (5,0) on y-axis is equidistant from (-1,2) and (3,4).
The co-ordinates of the mid point joining the points $(sin^2 \theta, sec^2 \theta )$ and $(cos^2 \theta - tan^2 \theta)$ is
The point on $X$-axis which is equidistant from the point $\left( 3,5 \right )$ and $\left( 4,2 \right )$ is
Let P be the point (1, 0) and Q a point on the curve ${ y }^{ 2 }=8x$. The locus of mid point of PQ is-
The co -ordinates of the midpoint of a line segment joining $ p(5,7) $ and $ Q (-3,3) $ are........
If Q is a variable point on $x^2=4y$ and O is the origin, the locus of mid point OQ is equation of
The locus of the mid point of the portion intercepted between the axes by the line $x{\,}cos\alpha+y{\,}sin{\,} \alpha=p$, where $p\inR$, is
Locus of the midpoints of the intercepts between the co-ordinate Axes by the lines passing through (a, 0) does not intersect
If the $1st$ point of trisection of AB is $(t, 2t)$ and the ends A, B move on $x$ and $y$ axis respectfully, then the focus of midpoint of AB is
I every points on the line $(a _{1}-a _{2})x+(b _{1}-b _{2}),y=c$ is equidistance from the points $(a _{1},b _{1})$ and $(a _{2},b _{2})$ then $2c=$
The line equally inclined to the coordinates axes and equidistant from points A(1, -2) and B(3, 4) is
Let $O$ be the origin and $A$ be a point on the curve $y^{2}=4x$. then locus of midpoint of $OA$ is
The midpoint of the interval in which $x^{2}-2(\sqrt{-x})^{2}-3<0$ is satisfied, is
A tangent to the circle $x^{2}+y^{2}=a^{2}$ meets the axes at points A and B. The locus of the mid point of AB is
If $A=(1, 2, 3)$ and $B(3, 5, 7)$ and P, Q are the points on AB such that AP$=$PQ$\neq$QB, then the mid point of PQ is?
The locus of the mid-point of a chord of the circle ${ x }^{ 2 }+{ y }^{ 2 }=4$ which subtends a right angle at the origin, is
The locus of the mid-point of that chord of parabola which subtends right angle on the vertex will be :
The locus of the mid-point of that chord of parabola which subtends right angle on the vertex will be
The locus of the middle points of chords of length $4$ on the circle $x^ {2}+y^ {2}=16$
If the coordinates of the mid-points of side $AB$ and $AC$ of $\triangle ABC$ are $D(3,5)$ and $E(-3,-3)$ respectively, the $BC=$
Find a point on the y-axis which equidistant from the points $A(6,5)$ and $B(-4,3)$
If $(-6,-4)$ and $(3,5)$ are the extremities of the diagonals of a parallelogram and $(-2,1)$ is its third vertex, then its fourth vertex is
The mid point of the line joining the points $\left( \log _ { 2 } 8 , \log _ { 4 } 16 \right)$ and $\left( \sin 90 ^ { \circ } , \cos \theta \right)$ is
A (a,b) and (0,0) are two fixed points, ${ M } _{ 1 }$ is the mid points of AB, ${ M } _{ 2 }$ is the midpoint of $A{ M } _{ 1 },{ M } _{ 3 }$ is the midpoint of $A{ M } _{ 2 }$ and so on then ${ M } _{ 5 }$ =in
If an triangle ABC, A = {1, 10}, circumference = $\left( -\dfrac { 1 }{ 3 } ,\dfrac { 2 }{ 3 } \right) $ and orthocenter = $\left( \dfrac { 11 }{ 3 } ,\dfrac { 4 }{ 3 } \right) $ then the co-ordinate of mid-point of side opposite to A is ________.
The coordinates of the middle point of the chord of circle ${ x }^{ 2 }+{ y }^{ 2 }-6x=2y-54=0$ which is cut off by the line $2x-5y+18=0$ are __________.
The point on X-axis which is equidistant from the point (3, 5) and (4, 2)
If $A(a, b)$ and $B(0, 0)$ are two fixed points. $M _1$ is the mid point of $\overline{AB}$, $M _2$ is the mid point of $\overline{AM _1}$, $M _3$ is the mid point of $\overline{AM _2}$ and so on, then $M _5$ is?
The co-ordinates of the mid point of segment $KR$, where $K(2.5, -4.3)$ and $R(-1.5, 2.7)$, are
Two points $(a, 3)$ and $(5, b)$ are the opposite vertices of a rectangle. If the coordinates $(x, y)$ of the other two vertices satisfy the relation $y = 2x + c$ where $c^{2}+ 2a -b =0$ then the value $c$ can be
The coordinates of the centre of a circle are $(-6,1.5)$. If the ends of a diameter are $(-3,y)$ and $(x, -2)$ then:
Mid-point of the line-segment joining the points $(-5,4)$ and $(9, -8)$ is:
Three consecutive vertices of a parallelogram are $(1, -2)$, $(3,6)$ and $(5,10)$. The coordinates of the fourth vertex are:
Find the coordinates of the centre of a circle, if the coordinates of the end points of a diameter being $(-3,8)$ and $(5,6)$.
The mid-point of a line segment is $(5,8)$. If one end point is $(3,5)$, find the second end point
The vertices of a parallelogram are $(3, -2)$, $(4,0)$, $(6, -3)$ and $(5, -5)$. The diagonals intersect at the point M. The coordinates of the point M are:
Find the mid-point of AB where A and B are the points $(-5, 11)$ and $(7,3)$, respectively.
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points $(-2, -1)$, $(1,0)$, $(4,3)$ and $(1,2)$ meet.
The mid-point of a line is $(-4,-2)$ and one end of the line is $(-6,4)$. The co-ordinates of the other end are
The end points of a diagonal of a parallelogram are $(1, 3)$ and $(5, 7)$, then the mid-point of the other diagonal is ..........
Calculate mid point of $A(5,\,3)$ and $B(9,\,8)$
Three vertices of rhombus taken in order are $(2, -1), (3, 4)$ and $(-2, 3)$. Find the fourth vertex.
What is the midpoints between the coordinates $(-1, 2)$ and $(-1, -6)$?
What is the midpoints between the coordinates $(0, -6)$ and $(4, -4)$?
Find the centre of circle, if the coordinates of two ends of diameter are $(-1, 7)$ and $(11, 5)$
Find the midpoint between the coordinates $(9, 3)$ and $(1, 1)$.
Find the value of $k$, so that $(2, 1)$ is the midpoint between $(1, k)$ and $(3, 1)$.
Find the midpoints between the coordinates $(2, 3)$ and $(1, 0)$
In the standard $(x,y)$ coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are $(-3,0)$ amd $(7,4)$?
Points $A(\sqrt {2}, 4), B(6, -\sqrt {3})$ and $C$ are collinear. If $B$ is the midpoint of line segment $AC$, approximately calculate the $(x, y)$ coordinates of point $C$.
A square is formed by the points $(4, 5), (12, 5), (12, -3)$ and $(4, -3)$. Find the coordinates of the point at which the diagonals of the square intersect.
Given point $A(-3, -8)$, if the midpoint of segment $AB$ is $(1, -5)$, calculate the coordinates of point $B$.
R is the midpoint of the segment $\bar{PT}$, and $Q$ is the midpoint of line segment $\bar{PR}$. If $S$ is a point between $R$ and $T$ such that the length of segment $\overline{QS}$ is $10$ and the length of segment $\overline{PS}$ is $19$, what is the length of segment $\overline{ST}$?
In the $xy$-coordinate plane, the coordinates of three vertices of a rectangle are $\left(1, 5\right)$, $\left(5, 2\right)$ and $\left(5, 5\right)$. What are the coordinates of the fourth vertex of the rectangle?
If $\left (\dfrac {a}{3}, 4\right )$ is the midpoint of the line segment joining $A (-6, 5)$ and $B(-2, 3)$, find $a$.
$A(-3,2)$ and $B(5,4)$ are the end points of a line segment, find the coordinates of the midpoints of the line segment.
If $(-2,3), (4,-3), (4,5)$ are mid-points of the sides of a triangle, find the coordinates of the centroid of the triangle formed by these mid-points.
Find the third vertex of a triangle, if two of its vertices are $(-3,1), (0,-2)$ and centroid is at the origin.
Find the midpoint of the line segment joining the points $(1,-1)$ and $(-5,-3)$
The centre of a circle is at $(-6,4)$. If one end of a diameter of the circle is at the origin, then find the other end.
Find the mid point of (3,8) and (9,4).
Find the mid point of $(4,6)$ and $(2,-6)$.
If mid point of the line segment joining (2a, 4) and (-2, 3b) is (1, 2a + 1), then the values of a and b are given by
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points $(-2,-1),(1,0),(4,3)$ and $(1,2)$ meet.
$P and Q$ are points on the line joining $A(-2,5) and (3,1)$ such that $AP=PQ=QB$ then the mid point of $PQ$ is ?
If $P \left( \dfrac{a}{3},\dfrac{b}{2} \right)$ is the mid-point of the line segment joining $A(-4,3)$ and $B(-2,4)$ then $(a,b)$ is
$A\equiv(0, b), B\equiv(0, 0) $ and $C\equiv(a, 0)$ are the vertices of $\triangle ABC. D, E, F$ are the mid-points of the sides $BC, CA $ and $AB $ respectively. If $a^{2}+ b^{2} = 20$ then
If two vertices of a parellelogram are $(3,2)$ and $(-1,0)$ and the diagonals intersect at $(2, -5)$, then the other two vertices are: