Question

name____________________ period 9/8/25 geometry day 3 hw (midpoint) show your work in the spaces provided to earn full credit 2 pts each 1. plot the midpoint of segment $overline{ab}$. then give its coordinates. 2. find the midpoint between $(4, - 7)$ and $(8,9)$. 3. give the coordinates of two endpoints whose midpoint does not have a whole number x - coordinate or y - coordinate. 4. point $m(5,-7)$ is the midpoint of $overline{cd}$. if $c$ is $(2, - 3)$, find the coordinates of $d$. 5. draw 2 line segments of different lengths that both have $m$ as a midpoint.

Explanation:

1.

• Without the coordinates of points A and B, we cannot plot the mid - point or give its coordinates.

2.

Step1: Recall mid - point formula

The mid - point formula between 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 $x_1 = 4,y_1=-7,x_2 = 8,y_2 = 9$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{4 + 8}{2}=\frac{12}{2}=6$

Step3: Calculate y - coordinate of mid - point

$y=\frac{-7+9}{2}=\frac{2}{2}=1$

Step1: Use mid - point formula

The mid - point formula between $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(2,3)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{1 + 2}{2}=\frac{3}{2}=1.5$

Step3: Calculate y - coordinate of mid - point

$y=\frac{2+3}{2}=2.5$

Step1: Use mid - point formula for x - coordinate

We know that for the mid - point $M(5,-7)$ of $\overline{CD}$ with $C(2,-3)$, the x - coordinate of the mid - point formula $\frac{2 + x}{2}=5$. Solving for $x$:
$2+x = 10$, so $x=8$.

Step2: Use mid - point formula for y - coordinate

The y - coordinate of the mid - point formula $\frac{-3 + y}{2}=-7$. Solving for $y$:
$-3 + y=-14$, so $y=-11$.

Answer:

The mid - point is $(6,1)$

3.

Let the two endpoints be $(1,2)$ and $(2,3)$.