Question

1. match the segment described on the left with its mid - point on the right.

segment endpoints\tmidpoint
a. g(4,7) and h(3, - 9)\t1. (2.5, - 2)
b. j(4,7) and k( - 3,9)\t2. (0.5,8)
c. l( - 4, - 7) and m(9,3)\t3. ( - 0.5,1)
d. n( - 4, - 7) and p(3,9)\t4. (3.5, - 1)

Explanation:

Step1: Recall mid - point formula

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

Step2: Calculate mid - point for A

For $G(4,7)$ and $H(3, - 9)$, $x=\frac{4 + 3}{2}=\frac{7}{2}=3.5$, $y=\frac{7+( - 9)}{2}=\frac{7 - 9}{2}=-1$. The mid - point is $(3.5,-1)$.

Step3: Calculate mid - point for B

For $J(4,7)$ and $K(-3,9)$, $x=\frac{4+( - 3)}{2}=\frac{4 - 3}{2}=0.5$, $y=\frac{7 + 9}{2}=8$. The mid - point is $(0.5,8)$.

Step4: Calculate mid - point for C

For $L(-4,-7)$ and $M(9,3)$, $x=\frac{-4 + 9}{2}=\frac{5}{2}=2.5$, $y=\frac{-7 + 3}{2}=\frac{-4}{2}=-2$. The mid - point is $(2.5,-2)$.

Step5: Calculate mid - point for D

For $N(-4,-7)$ and $P(3,9)$, $x=\frac{-4 + 3}{2}=-0.5$, $y=\frac{-7 + 9}{2}=1$. The mid - point is $(-0.5,1)$.

Answer:

A. $(3.5,-1)$
B. $(0.5,8)$
C. $(2.5,-2)$
D. $(-0.5,1)$