Question

UV has the endpoints U(0, 3) and V(–4, –5). Which shows the correct calculation for finding the x-coordinate of the point that partitions the line segment into a 4:3 ratio?

x = (–4)
x = (–4)
x = (–5 – 3) + 3
x = (–5 – 3) – 5

Answer 1

Use the section formula or parametric form. If U(0,3) and V(−4,−5) and the point P divides UV so UP:PV = 4:3, then

x = (3·0 + 4·(−4)) / (4+3) = (0 − 16)/7 = −16/7.

Equivalently x = 0 + (4/7)(−4) = −16/7.