Question

The distance, d, between two points, (x1,y1) and (x2,y2), can be found using the formula d=√(x2−x1)^2+(y2−y1)^2

How can you rearrange the given formula to correctly find y2?

Answer 1

square both sides of d=√(x2−x1)^2+(y2−y1)^2
d^2 = x2^2 - 2(x2)(x1) + x1^2 + y2^2 - 2(y2)(y1) + y1^2
d^2 - x2^2 + 2(x2)(x1) - x1^2 - y1^2 = y2^2 - 2(y2)(y1)
y2^2 - 2(y2)(y1) - d^2 + x2^2 - 2(x2)(x1) + x1^2 - y1^2 = 0
compare with the standard quadratic, we have
a = 1
b = -2y1
c = - d^2 + x2^2 - 2(x2)(x1) + x1^2 - y1^2

Now solve for y2 using the quadratic equation, rather unruly mess

Answer 2

the distance between the points x ,y and x,y two is give by