Question

Find the relation between x and y if thr points A(x,y) , B(-5,7) and C(-4,5) are collinear. if $\tan (A-B)=1/\sqrt{3}$ and $\tan (A+B)=\sqrt{3}$ , find A and B.

Answer 1

if points are colinear then slopes are equal

$\frac{y-7}{x+5}=-2$

$2x+y=-3$

$\frac{5-y}{-4-x}=-2$

$x+y=-3$

by solving both equations $x=0,y=-3$

$tan(A-B)=1/\sqrt{3}$

$A-B=30$

$tan(A+B)=\sqrt{3}$

$A+B=60$

by solving both equations $A=45,B=15$