Question

PLEASE HELP

Point A is at (1,5) and point C is at (-5, – 7).
Find the coordinates of point B on AC such that AC is 6 times as long as AB.

Answer 1

(0,3)

Explanation:

This is a problem from affine geometry, so doesn’t need any concept of distance that mixes x and y coordinates. We can just take each coordinate separately.

(1,5),(−5,−7),(,),=6

Usually in these sorts of problems with unknown B we’re given the ratio AB:BC; here we have the slightly unusual and easier AB:AC.

The difference of the given points −=(6,12) .

Since =6 we know −=16(−)=(1,2)

So =−(1,2)=(1,5)−(1,2)

=(0,3)