Question

1. find the midpoint between each pair of points. (-1, -5) and (-5, 9) 16. (7, -2) and (-4, 2) 17. if m is the midpoint of $overline{xy}$, find the coordinates of x if m(-3, -1) and y(-8, 6). 18. if r is the midpoint of $overline{qs}$, qr = 8x - 51 and rs = 3x - 6, find qs.

Explanation:

15.

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $(x_1,y_1)=(-1,-5)$ and $(x_2,y_2)=(-5,9)$.

Step2: Calculate the x - coordinate of the mid - point

$x=\frac{-1+( - 5)}{2}=\frac{-1 - 5}{2}=\frac{-6}{2}=-3$.

Step3: Calculate the y - coordinate of the mid - point

$y=\frac{-5 + 9}{2}=\frac{4}{2}=2$.

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $(x_1,y_1)=(7,-2)$ and $(x_2,y_2)=(-4,2)$.

Step2: Calculate the x - coordinate of the mid - point

$x=\frac{7+( - 4)}{2}=\frac{7 - 4}{2}=\frac{3}{2}=1.5$.

Step3: Calculate the y - coordinate of the mid - point

$y=\frac{-2 + 2}{2}=0$.

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 $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(-3,-1)$ and $Y(-8,6)$. Let the coordinates of $X$ be $(x,y)$. Then $\frac{x+( - 8)}{2}=-3$.

Step2: Solve for x

Multiply both sides of the equation $\frac{x - 8}{2}=-3$ by 2: $x-8=-6$. Add 8 to both sides: $x=-6 + 8=2$.

Step3: Use mid - point formula for y - coordinate

$\frac{y + 6}{2}=-1$.

Step4: Solve for y

Multiply both sides of the equation $\frac{y + 6}{2}=-1$ by 2: $y+6=-2$. Subtract 6 from both sides: $y=-2-6=-8$.

Answer:

$(-3,2)$

16.