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 two over three the distance from point P to point R

  7/3

Step-by-step explanation:

The distances have the ratio ...

  (Q -P) = (2/3)(R -P)

  Q = P +(2/3)R -(2/3)P = (2R +P)/3

  Qy = (2Ry +Py)/3 = (2·0 +7)/3 = 7/3

your answer would be 12

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4