Question

1. find the distance between the coordinates (2, 3) and (-7, 0). *

your answer

1. the midpoint of line eg is at f(6, 8). if point e is located at (4, 0), where would point g be? *

your answer

1. find the midpoint between the coordinates (-5, -3) and (-3, 0). *

your answer

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(-7,0)$.

Step2: Substitute values

$d=\sqrt{(-7 - 2)^2+(0 - 3)^2}=\sqrt{(-9)^2+(-3)^2}=\sqrt{81 + 9}=\sqrt{90}=3\sqrt{10}$

Step3: Recall mid - point formula for finding an endpoint

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 $G$ be $(x,y)$. We know that $\frac{4 + x}{2}=6$ and $\frac{0 + y}{2}=8$.

Step4: Solve for $x$ and $y$ of point $G$

For the $x$ - coordinate: $\frac{4 + x}{2}=6$, then $4+x = 12$, so $x=8$. For the $y$ - coordinate: $\frac{0 + y}{2}=8$, then $y = 16$. So the coordinates of $G$ are $(8,16)$.

Step5: Recall mid - point formula for finding mid - point

For two points $(x_1,y_1)=(-5,-3)$ and $(x_2,y_2)=(-3,0)$, the mid - point $M=(\frac{-5+( - 3)}{2},\frac{-3 + 0}{2})$.

Step6: Calculate mid - point

$M=(\frac{-5-3}{2},\frac{-3}{2})=(-4,-\frac{3}{2})$

Answer:

1. $3\sqrt{10}$
2. $(8,16)$
3. $(-4,-\frac{3}{2})$