Question

Given directed line segment PR below, find the coordinates of Q on PR

Answer 1

Answer:

$(\frac{4}{3},-3)$

Step-by-step explanation:

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ($x_1,y_1$) and B($x_2,y_2$) is given by the formula:

$x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1$

From the graph, the location of the point is P(2, 5), R(1, -7). Let point Q be (x, y) which divides PR in ratio 2:1. Coordinates of point Q is at:

$x=\frac{a}{a+b}(x_2-x_1)+x_1=\frac{2}{2+1}(1-2)+2=\frac{2}{3}(-1)+2=\frac{4}{3} \\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1=\frac{2}{2+1}(-7-5)+5= \frac{2}{3}(-12)+5=-3$

Point Q is at $(\frac{4}{3},-3)$