Question

midpoint and distance formulas
find the midpoint of the line segment with the given endpoints.

1. (-4, -2), (3, 3)
2. (-1, 0), (-3, -4)

find the other endpoint of the line segment with the given endpoint and midpoint.

1. endpoint: (-5, 4), midpoint: (-10, -6)
2. endpoint: (-8, 8), midpoint: (5, -3)

find the midpoint of each line segment.
5)
6)

Explanation:

1. For endpoints $(-4,-2)$ and $(3,3)$

Step1: Use mid - point formula for x - coordinate

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For the x - coordinate, $x_1=-4$ and $x_2 = 3$. So, $x=\frac{-4 + 3}{2}=\frac{-1}{2}=-0.5$.

Step2: Use mid - point formula for y - coordinate

For the y - coordinate, $y_1=-2$ and $y_2 = 3$. So, $y=\frac{-2+3}{2}=\frac{1}{2}=0.5$.

Step1: Calculate x - coordinate of mid - point

Using the mid - point formula $x=\frac{x_1 + x_2}{2}$, with $x_1=-1$ and $x_2=-3$. Then $x=\frac{-1+( - 3)}{2}=\frac{-4}{2}=-2$.

Step2: Calculate y - coordinate of mid - point

Using the mid - point formula $y=\frac{y_1 + y_2}{2}$, with $y_1 = 0$ and $y_2=-4$. Then $y=\frac{0+( - 4)}{2}=\frac{-4}{2}=-2$.

Step1: Find the other x - coordinate

Let the unknown endpoint be $(x,y)$. Using the mid - point formula for x - coordinates $\frac{-5 + x}{2}=-10$. Cross - multiply: $-5+x=-20$. Solve for $x$: $x=-20 + 5=-15$.

Step2: Find the other y - coordinate

Using the mid - point formula for y - coordinates $\frac{4 + y}{2}=-6$. Cross - multiply: $4 + y=-12$. Solve for $y$: $y=-12 - 4=-16$.

Answer:

$(-0.5,0.5)$

2. For endpoints $(-1,0)$ and $(-3,-4)$