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 $overline{rt}$. compute rt. please remember that \ab\ translates to \the length of segment ab\. so please use the distance formula.

Explanation:

Step1: Identify the 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: Determine the coordinates of R and T

Given $R(-10,-4)$ and $T(-2,2)$, so $x_1=-10,y_1 = - 4,x_2=-2,y_2 = 2$.

Step3: Substitute values into the formula

$RT=\sqrt{(-2-(-10))^2+(2 - (-4))^2}=\sqrt{(-2 + 10)^2+(2 + 4)^2}=\sqrt{(8)^2+(6)^2}$.

Step4: Calculate the squares and sum

$\sqrt{64 + 36}=\sqrt{100}$.

Step5: Find the square - root

$\sqrt{100}=10$.

Answer:

$10$