Question

1. find the midpoint between the points (-2, 3) and (-7, -7) (-4.5,-2) 4. the midpoint of line eg is at f(1, 10). if point e is located at (6, -2), where would point g be? your answer 5. find the distance between the points (-4, -3) and (-1, 1). your answer 6. find the midpoint between the points (-4, -3) and (-1, 1). * -2.5, -1

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 problem 3

For points $(-2,3)$ and $(-7,-7)$, $x_1=-2,y_1 = 3,x_2=-7,y_2=-7$.
$x=\frac{-2+( - 7)}{2}=\frac{-2 - 7}{2}=\frac{-9}{2}=-4.5$
$y=\frac{3+( - 7)}{2}=\frac{3 - 7}{2}=\frac{-4}{2}=-2$

Step3: Solve problem 4

Let the coordinates of point $G$ be $(x,y)$. Using the mid - point formula, $\frac{6 + x}{2}=1$ and $\frac{-2 + y}{2}=10$.
For $\frac{6 + x}{2}=1$, we have $6+x = 2$, so $x=2 - 6=-4$.
For $\frac{-2 + y}{2}=10$, we have $-2 + y=20$, so $y=20 + 2=22$. So point $G$ is $(-4,22)$.

Step4: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step5: Solve problem 5

For points $(-4,-3)$ and $(-1,1)$, $x_1=-4,y_1=-3,x_2=-1,y_2 = 1$.
$d=\sqrt{(-1-( - 4))^2+(1-( - 3))^2}=\sqrt{(-1 + 4)^2+(1 + 3)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$

Step6: Solve problem 6

For points $(-4,-3)$ and $(-1,1)$, $x_1=-4,y_1=-3,x_2=-1,y_2 = 1$.
$x=\frac{-4+( - 1)}{2}=\frac{-4 - 1}{2}=\frac{-5}{2}=-2.5$
$y=\frac{-3 + 1}{2}=\frac{-2}{2}=-1$

Answer:

1. $(-4.5,-2)$
2. $(-4,22)$
3. $5$
4. $(-2.5,-1)$