Question

one of the endpoints of line segment ab is a(-6,2). determine the coordinates of point b if the midpoint of the segment is m(7/2, -3/2).

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 $x_1=-6,y_1 = 2$, and $M(\frac{7}{2},-\frac{3}{2})$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=\frac{7}{2}$. Substitute $x_1=-6$ into the equation: $\frac{-6 + x_2}{2}=\frac{7}{2}$. Cross - multiply: $-6+x_2 = 7$. Then $x_2=7 + 6=13$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-\frac{3}{2}$. Substitute $y_1 = 2$ into the equation: $\frac{2 + y_2}{2}=-\frac{3}{2}$. Cross - multiply: $2+y_2=-3$. Then $y_2=-3 - 2=-5$.

Answer:

$(13,-5)$