Question

(a) What is the slope of the line joining the points $A(2,-3)$ and $B(6,3)$? Find the equation of this line.
(b) Find the co-ordinates of the point $C$ at which the line cuts the x-axis.
(c) Show that $C$ is the mid-point of the line $AB$.

Answer 1

(a)Slope=$\frac{Y_2-Y_1}{X_2-X_1}$

$=\frac{3+3}{6-2}=\frac{6}{4}=\frac{3}{2}$

(b) equation of line

$y+3=\frac{3}{2}(x-2)$

$3x-2y=12$

On X axis y-coordinate is $0$

So we get $3x=12$

$x=4$

Coordinate of C $=(4,0)$

(c) Mid point of AB$=(\frac{2+6}{2},\frac{-3+3}{2})=(4,0)$

Thus C is mid point of AB