Question

point a is at (-7 5) and point c is at (5 -1). find the coordinates of point b on line ab such that ab is 5 times as long as bc

Answer 1

Step-by-step explanation:

Let the coordinates of point b be (x,y).

Given the coordinates of a (-7,5) and c(5,-1)

Now according to question

ab = 5bc

using distance formula

$\sqrt{(x+7)^2+(y-5)^2} =5\sqrt{(5-x)^2+(-1-y)^2}$

Solving we can get

$x=-\frac{-11+\sqrt{-4y^2-10y+25}}{2},\:x=\frac{\sqrt{-4y^2-10y+25}+11}{2}$'

However, we do need either x or y coordinate of point b to find the other.