Question

1. given the coordinates in the boxes and m is the midpoint of qs, what are the values of a and b?

points x y
q -5 a
m 3 5
s b 9
a =
b =

Explanation:

Step1: Use mid - point formula for x - coordinates

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M_x=\frac{x_1 + x_2}{2}$. Here, for points $Q(-5,a)$ and $S(b,9)$ with mid - point $M(3,5)$, for the x - coordinates: $\frac{-5 + b}{2}=3$.

Step2: Solve for b

Multiply both sides of the equation $\frac{-5 + b}{2}=3$ by 2: $-5 + b=6$. Then add 5 to both sides: $b=6 + 5=11$.

Step3: Use mid - point formula for y - coordinates

The mid - point formula for the y - coordinates is $M_y=\frac{y_1 + y_2}{2}$. So, $\frac{a + 9}{2}=5$.

Step4: Solve for a

Multiply both sides of the equation $\frac{a + 9}{2}=5$ by 2: $a+9 = 10$. Then subtract 9 from both sides: $a=10 - 9=1$.

Answer:

$a = 1$
$b = 11$