Question

question 3 of 10
one of the endpoints of line - segment ab is a(-9,-14)
determine the coordinates of point b if the mid - point of the
segment is m(\frac{5}{2},\frac{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 $A(-9,-4)$, $M(\frac{5}{2},\frac{7}{2})$, and we need to find $B(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1=-9$ and $x_M = \frac{5}{2}$, we get $\frac{-9 + x_2}{2}=\frac{5}{2}$. Cross - multiply: $-9 + x_2=5$. Then $x_2=5 + 9=14$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1=-4$ and $y_M=\frac{7}{2}$, we get $\frac{-4 + y_2}{2}=\frac{7}{2}$. Cross - multiply: $-4 + y_2=7$. Then $y_2=7 + 4 = 11$.

Answer:

$(14,11)$