Tag: quadrants

The Cartesian plane consists of two perpendicular and directed lines whose intersection point is the zero point for both the lines.

x - axis and y- axis intersect at the origin. SO, point of intersection is (0,0)

Since the x coordinate of the point is 0, its on the y axis.

The horizontal axis is called x-axis.

x and y coordinates are required to represent a point in cartesian plane.

i) The x-axis ,a line parallel to it is called horizontal line

The equation of line $y$=0 represents $x$ -axis ie.$(x,y)$ = $(x,0)$

$\dfrac {y _{2} - y _{1}}{x _{2} - x _{1}} = \dfrac {-4}{3} =\dfrac{3+5}{-5-x}=\dfrac{-4}{3}$

The smallest possible value of $\overline {AC} + \overline {BC}$ is obtained when $C$ is the intersection of the y-axis, with the line that leads from $A$ to the mirror image the mirror being the y-axis) $B' : (-2, 1)$ of $B$. This is true because $\overline {CB'} = \overline {CB}$ and a straight line is the shortest path between two points. The line through and $B'$ given by
$y = \dfrac {5 - 1}{5 + 2} x + k = \dfrac {4}{7} x + k$.
To find $k$, we use the fact that the line goes through $A$:
$5 = \dfrac {4}{7} . 5 + k, k = 5 - \dfrac {20}{7} = \dfrac {15}{7} = 2\dfrac {1}{7}$;
$\therefore C$ has coordinates $(0, 2\dfrac {1}{7})$.

The triangle cannot be equilateral if coordinates of vertices of the triangle is always rational.