Question

directions: find the midpoint between the two given points. 5. (-4,4) and (5,-1) 6. (-1,-6) and (-6,5) 7. (2,4) and (1,-3) 8. (-4,4) and (-2,2)

Explanation:

Step1: Recall mid - point formula

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

Step2: Solve for problem 5

For points $(-4,4)$ and $(5,-1)$, $x_1=-4$, $y_1 = 4$, $x_2=5$, $y_2=-1$.
$x$ - coordinate of mid - point: $\frac{-4 + 5}{2}=\frac{1}{2}$
$y$ - coordinate of mid - point: $\frac{4+( - 1)}{2}=\frac{3}{2}$
The mid - point is $(\frac{1}{2},\frac{3}{2})$.

Step3: Solve for problem 6

For points $(-1,-6)$ and $(-6,5)$, $x_1=-1$, $y_1=-6$, $x_2=-6$, $y_2 = 5$.
$x$ - coordinate of mid - point: $\frac{-1+( - 6)}{2}=\frac{-7}{2}$
$y$ - coordinate of mid - point: $\frac{-6 + 5}{2}=-\frac{1}{2}$
The mid - point is $(-\frac{7}{2},-\frac{1}{2})$.

Step4: Solve for problem 7

For points $(2,4)$ and $(1,-3)$, $x_1=2$, $y_1 = 4$, $x_2=1$, $y_2=-3$.
$x$ - coordinate of mid - point: $\frac{2 + 1}{2}=\frac{3}{2}$
$y$ - coordinate of mid - point: $\frac{4+( - 3)}{2}=\frac{1}{2}$
The mid - point is $(\frac{3}{2},\frac{1}{2})$.

Step5: Solve for problem 8

For points $(-4,4)$ and $(-2,2)$, $x_1=-4$, $y_1 = 4$, $x_2=-2$, $y_2=2$.
$x$ - coordinate of mid - point: $\frac{-4+( - 2)}{2}=\frac{-6}{2}=-3$
$y$ - coordinate of mid - point: $\frac{4 + 2}{2}=3$
The mid - point is $(-3,3)$.

Answer:

1. $(\frac{1}{2},\frac{3}{2})$
2. $(-\frac{7}{2},-\frac{1}{2})$
3. $(\frac{3}{2},\frac{1}{2})$
4. $(-3,3)$