Question

qe 7 find the coordinates of a if m(-1,2) is the mid - point of segment ab and b has coordinates of (3,-5). a( , )

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 $A=(x,y)$ and $B=(3,-5)$ and $M=(-1,2)$.

Step2: Solve for x - coordinate of A

We have $\frac{x + 3}{2}=-1$. Multiply both sides by 2: $x + 3=-2$. Then subtract 3 from both sides: $x=-2 - 3=-5$.

Step3: Solve for y - coordinate of A

We have $\frac{y+( - 5)}{2}=2$. Multiply both sides by 2: $y-5 = 4$. Then add 5 to both sides: $y=4 + 5=9$.

Answer:

$(-5,9)$