Question

use the given endpoint a and midpoint m of line segment ab to find the coordinates of the y - value of the endpoint b. a(22, - 19) m(10, 24) b(-2, y)

Explanation:

Step1: Recall mid - point formula for y - coordinate

The mid - point formula for the y - coordinate of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ and mid - point $(x_m,y_m)$ is $y_m=\frac{y_1 + y_2}{2}$. Here, $y_1=-19$, $y_m = 24$, and $y_2=y$.

Step2: Substitute values into formula

We have $24=\frac{-19 + y}{2}$.

Step3: Solve for y

Multiply both sides of the equation by 2: $24\times2=-19 + y$. So, $48=-19 + y$. Then add 19 to both sides: $y=48 + 19$.

Answer:

$y = 67$