Question

Find the point of intersection of a line passing through $(5,3)\&(3,5)$ by a line $x-y=2$.

• A. $(5,5)$
• B. $(3,3)$
• C. $(5,3)$
• D. $(3,5)$

Answer 1

The correct option is C $(5,3)$

Given,
Consider $A(5,3)\&B(3,5)$ & line $x-y=2$

Equation of line given the slope $m$ is
$y-y_1=m(x-x_1)$

Slope is given by, $m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-3}{3-5}=-1$

Equation of $AB,$ $y-3=-1(x-5)\Rightarrow x+y=8$

By solving we can find the point of intersection (or common point)

$x+y=8\underset{–}{x-y=2}2x=10\Rightarrow x=55+y=8\Rightarrow y=3$

The point is $(5,3)$