Find the coordinates of P, a point 1/4 of the distance from C(-2,4) to D(4,3).

Question

I know what the correct answer is but I had to subtract the y coordinate after multiplying the fractional distance when the "formula" says to add the fractional distance to the first coordinate. If you do that you end up with a point not on the line. I don't understand why,

Answer 1

desmos.com/calculator/sej8jwevh4

You can move the origin and target points to different locations and change the fractional value for k.

Answer 2

For details please see ParagonMath.com/1/1.png and ParagonMath.com/1/2.png

Essentially, from calculations there are two points P1 (-7/2 , 17/4) and P2 (-1/2 , 15/4).

Only P2 is correct and on the CD line. The explanation for the other point: we raised to ^2, which introduced a new incorrect solution.