Question

Determine 'x' so that the line passing through (3, 4) and (x, 5) makes ${135}^{\circ }$ angle with the positive direction of x-axis.

Answer 1

Given that the line passes $A(3,4)$ & $B(x,5)$

Hence, $x_1=3,x_2=x,y_1=4,y_2=5$

slope = $m=tan\left(1350\right)$

$=tan(90+45)$

$=-cot\left(45\right)$

$=-1$

$m=\frac{(y_2-y_1)}{x_2-x_1}$

$-1=\frac{(5-4)}{(x-3)}$

$3-x=5-4$

$x=1-3$

$x=-2$