Question

1. find the midpoint for each segment with the given endpoints.

a. c(-2, 5) and d(8, -12)
b. e(2.5, -7) and f(-6.2, -3.8)
find the other endpoint
find the coordinates of a if m(-1,2) is the midpoint of ab
you try: find the other endpoint given one endpoint
a) midpoint: (-5, 10)
endpoint: (-8, 6)

Explanation:

Step1: Recall mid - point formula

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

a. For points $C(-2,5)$ and $D(8,-12)$

Step1: Calculate x - coordinate of mid - point

$x=\frac{-2 + 8}{2}=\frac{6}{2}=3$

Step2: Calculate y - coordinate of mid - point

$y=\frac{5+( - 12)}{2}=\frac{5 - 12}{2}=\frac{-7}{2}=-3.5$
The mid - point of $\overline{CD}$ is $(3,-3.5)$.

b. For points $E(2.5,-7)$ and $F(-6.2,-3.8)$

Step1: Calculate x - coordinate of mid - point

$x=\frac{2.5+( - 6.2)}{2}=\frac{2.5-6.2}{2}=\frac{-3.7}{2}=-1.85$

Step2: Calculate y - coordinate of mid - point

$y=\frac{-7+( - 3.8)}{2}=\frac{-7 - 3.8}{2}=\frac{-10.8}{2}=-5.4$
The mid - point of $\overline{EF}$ is $(-1.85,-5.4)$.

Find the other endpoint:

Let the coordinates of $A$ be $(x_1,y_1)$, the coordinates of $B$ be $(x_2,y_2)$ and the mid - point $M(-1,2)$.
We know that $\frac{x_1 + x_2}{2}=-1$ and $\frac{y_1 + y_2}{2}=2$. But we don't have the coordinates of $B$, so we can't solve this part without more information.

YOU TRY:

Let the mid - point $M(-5,10)$ and one endpoint $A(-8,6)$. Let the other endpoint be $(x,y)$.

Step1: Use x - coordinate formula

$\frac{-8 + x}{2}=-5$
Multiply both sides by 2: $-8 + x=-10$
Add 8 to both sides: $x=-10 + 8=-2$

Step2: Use y - coordinate formula

$\frac{6 + y}{2}=10$
Multiply both sides by 2: $6 + y = 20$
Subtract 6 from both sides: $y=20 - 6 = 14$
The other endpoint is $(-2,14)$.

Answer:

a. Mid - point of $\overline{CD}$: $(3,-3.5)$
b. Mid - point of $\overline{EF}$: $(-1.85,-5.4)$
YOU TRY: Other endpoint: $(-2,14)$