Question

1. find the coordinates of a if m(-1, 2) is the midpoint of ab and b has coordinates of (3, -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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(x_1,y_1)$ and $B(3,-5)$ and $M(-1,2)$.

Step2: Solve for $x_1$

We know that $\frac{x_1 + 3}{2}=-1$. Cross - multiply: $x_1+3=-2$. Then $x_1=-2 - 3=-5$.

Step3: Solve for $y_1$

We know that $\frac{y_1+( - 5)}{2}=2$. Cross - multiply: $y_1-5 = 4$. Then $y_1=4 + 5=9$.

Answer:

$(-5,9)$