Question

1. given (a(-3,8)), find the coordinates of the point (b) such that (c(5, - 10)) is the mid - point of segment (ab)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(x_1,y_1)=(-3,8)$ and $B(x_2,y_2)$ and the mid - point $C(x_m,y_m)=(5,-10)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $5=\frac{-3 + x_2}{2}$. Cross - multiply: $5\times2=-3 + x_2$. So, $10=-3 + x_2$. Then $x_2=10 + 3=13$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $-10=\frac{8 + y_2}{2}$. Cross - multiply: $-10\times2=8 + y_2$. So, $-20=8 + y_2$. Then $y_2=-20 - 8=-28$.

Answer:

$(13,-28)$