Question

the midpoint of a (11, 12) and b (x, y) is (2, 17). what is b?
(13,29)
(-9, 5)
(-7, 22)
(6, 6)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $(x_1,y_1)=(11,12)$ and the mid - point is $(2,17)$.

Step2: Solve for x - coordinate of B

We have $\frac{11 + x}{2}=2$. Cross - multiply: $11 + x=4$. Then $x=4 - 11=-7$.

Step3: Solve for y - coordinate of B

We have $\frac{12 + y}{2}=17$. Cross - multiply: $12 + y = 34$. Then $y=34 - 12 = 22$.

Answer:

C. (-7, 22)