Question

1. find the distance between the points (-2, 3) and (-7, -7) 1 point 11.2 2. find the distance between the points (-4, 5) and (-1, 1). 1 point your answer this is a required question 3. find the midpoint between the points (-2, 3) and (-7, -7) 1 point (-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? 1 point

Explanation:

Step1: Recall distance formula

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

Step2: Identify points for second - distance problem

For points $(-4,5)$ and $(-1,1)$, let $(x_1,y_1)=(-4,5)$ and $(x_2,y_2)=(-1,1)$.

Step3: Substitute values into formula

$d=\sqrt{(-1-(-4))^2+(1 - 5)^2}=\sqrt{(3)^2+(-4)^2}$.

Step4: Calculate values inside square - root

$\sqrt{9 + 16}=\sqrt{25}$.

Step5: Find the square root

$d = 5$.

Step6: Recall mid - point formula for fourth problem

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $G$ be $(x,y)$. Given the mid - point $F(1,10)$ and point $E(6,-2)$.

Step7: Set up equations for $x$ and $y$ coordinates

For the $x$ - coordinate: $\frac{6 + x}{2}=1$, which gives $6+x = 2$, so $x=-4$. For the $y$ - coordinate: $\frac{-2 + y}{2}=10$, which gives $-2 + y=20$, so $y = 22$.

Answer:

1. Distance between $(-4,5)$ and $(-1,1)$: $5$
2. Coordinates of point $G$: $(-4,22)$