Question

one of the endpoints of line segment ab is a(0, -9). determine the coordinates of point b if the midpoint of the segment is m(-2, -5).

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $A(0,-9)$ with $x_1 = 0$ and $y_1=-9$, and $M(-2,-5)$ with $x_M=-2$ and $y_M = - 5$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substitute $x_1 = 0$ and $x_M=-2$ into the formula: $\frac{0 + x_2}{2}=-2$. Multiply both sides by 2: $0 + x_2=-4$, so $x_2=-4$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substitute $y_1=-9$ and $y_M=-5$ into the formula: $\frac{-9 + y_2}{2}=-5$. Multiply both sides by 2: $-9 + y_2=-10$. Add 9 to both sides: $y_2=-1$.

Answer:

$(-4,-1)$