Question

1. find the distance between the coordinates (4, 1) and (2, 5). *

your answer

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

-4, -3/2

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

your answer

this is a required question

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

your answer

Explanation:

7.

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, $x_1 = 4,y_1 = 1,x_2=2,y_2 = 5$.

Step2: Substitute values

$d=\sqrt{(2 - 4)^2+(5 - 1)^2}=\sqrt{(-2)^2+4^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}$

Step1: Recall distance formula

Use $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ with $x_1 = 2,y_1 = 3,x_2=-7,y_2 = 0$.

Step2: Substitute values

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

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $E(x_1,y_1)=(4,0)$ and $F(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})=(6,8)$ and $G(x_2,y_2)$.

Step2: Solve for $x_2$

$\frac{4+x_2}{2}=6$, then $4+x_2 = 12$, so $x_2=8$.

Step3: Solve for $y_2$

$\frac{0 + y_2}{2}=8$, then $y_2 = 16$.

Answer:

$2\sqrt{5}$

8.