Question

a line segment is drawn on a coordinate plane with the endpoints r(-10, -4) and s(10, 11). point t(-2, 2) is also on $overline{rs}$. compute ts.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify coordinates for points T and S

For points $T(-2,2)$ and $S(10,11)$, $x_1=-2,y_1 = 2,x_2=10,y_2 = 11$.

Step3: Substitute values into formula

$TS=\sqrt{(10-(-2))^2+(11 - 2)^2}=\sqrt{(10 + 2)^2+(9)^2}=\sqrt{144+81}=\sqrt{225}$.

Step4: Simplify the square - root

$\sqrt{225}=15$.

Answer:

15