Question

question 8 of 10
one of the endpoints of line segment ab is a(-9,-14). determine the coordinates of point b if the midpoint of the segment is m(-5/2,7/2)

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 $x_1=-9,y_1 = - 14$ and $M(-\frac{5}{2},\frac{7}{2})$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-\frac{5}{2}$. Substitute $x_1=-9$ into the equation: $\frac{-9 + x_2}{2}=-\frac{5}{2}$. Cross - multiply: $-9 + x_2=-5$. Then $x_2=-5 + 9=4$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=\frac{7}{2}$. Substitute $y_1=-14$ into the equation: $\frac{-14 + y_2}{2}=\frac{7}{2}$. Cross - multiply: $-14 + y_2=7$. Then $y_2=7 + 14 = 21$.

Answer:

$(4,21)$