Answer to Question #158359 in Analytic Geometry for Kathy

Question

find the points which trisect the segment joining the points (-3, 5) and (9, 2)

Answer 1

The trisect of $(x_1,y_1)$ and $(x_2,y_2)$ is $(x',y')$ and $(x'',y'')$ such that

$x'=\frac{x_1+2x_2}{3},\ y'=\frac{y_1+2y_2}{3},\ x''=\frac{2x_1+x_2}{3},\ y''=\frac{2y_1+y_2}{3}.$

In our case, $x_1=-3,\ y_1=5,\ x_2=9,\ y_2=2$

$x'=\frac{-3+2\cdot 9}{3}=5,\ y'=\frac{5+2\cdot 2}{3}=3,\ x''=\frac{2(-3)+9}{3}=1,\ y''=\frac{2\cdot 5+2}{3}=4.$

The points which trisect the segment joining the points $(-3, 5)$ and $(9, 2)$ are $(5,3)$ and $(1,4).$