Question

if the point (x,y) is equidistant from the point (a+b,b -a) and(a-b,a+b) prove that bx = ay​

Answer 1

Answer:

Step-by-step explanation:

An equidistant from the point means midpoint. Coordinates of a midpoint are

[($x_{1}$ + $x_{2}$) / 2 , ($y_{1}$ + $y_{2}$) / 2]

x = (a + b + a - b) / 2 ⇒ x = a

y = (b - a + a + b) / 2 ⇒ y = b

$\frac{x}{y}$ = $\frac{a}{b}$

After cross multiplication we have

bx = ay