Geometry help please

Question

Point P is located at (-2,7) and point R is located at (1,0). Find the y value for the point Q that is located 2/3 the distance from point P to point R.

Answer 1

An approach from linear algebra is the best approach here.

The y component of point located on the path from P to R a fraction , f, of the way from P to R is

y = 7 + f ( 0 -7 ) {this is the y component of P + f ( difference of y components of R and P)

For this problem point Q is 2/3 of the way, so f = 2/3

So the y component of Q is 7 + (2/3) ( -7) = 7/3