Question 1203786
Find the point (𝑥,𝑦)
on the line 𝑦=𝑥
that is equidistant from the pointsA (10,−10)
and B(−4,6)

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

{{{Distance = sqrt((x1-x2)^2 + (y1 - y2)^2)}}}
Square both sides andplug the given values

(x+4)^2+(y-6)^2=  (x-10)^2+(y+10)^2

expand

x^2+8x+16 +y^2-12y+36 = x^2-20x+100 +y^2+20y+100


8x+16-12y+36 = -20x +100+20y+100
combine like terms

28x-32y =148  but x=y

-4x = 148

x=37   ---> y=37

(37,37)

point (x, y) that is equidistant from the points (10, -10) and (-4, 6) is indeed (37, 37).