Question

SOLVE PLEASE! (Help)

Answer 1

Answer:

1. $\sqrt{218}$

2. $\sqrt{89}$

3. $2\sqrt{17}$

Step-by-step explanation:

The formula to find the distance between any two points on a coordinate plane is as follows:

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Where ($(x_1,y_1)$) and ($(x_2,y_2)$) are the two points one is trying to find the distance between. Substitute the points in and solve for the distance between them for each respective problem.

1.

Points: $(-4, 6),\ \ (3, -7)$

Substitute into the formula,

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{((-4)-(3))^2+((6)-(-7))^2}$

Simplify,

$D=\sqrt{((-4)-(3))^2+((6)-(-7))^2}$

$D=\sqrt{(-4-3)^2+(6+7)^2}$

$D=\sqrt{(-7)^2+(13)^2}$

$D=\sqrt{49+169}$

$D=\sqrt{218}$

2.

Points: $(-6, -5)\ \ (2,0)$

Substitute into the formula,

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{((-6)-(2))^2+((-5)-(0))^2}$

Simplify,

$D=\sqrt{((-6)-(2))^2+((-5)-(0))^2}$

$D=\sqrt{(-6-2)^2+(-5-0)^2}$

$D=\sqrt{(-8)^2+(-5)^2}$

$D=\sqrt{64+25}$

$D=\sqrt{89}$

3.

Points: $(-1, 4)\ \ (1,-4)$

Substitute into the formula,

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{((-1)-(1))^2+((4)-(-4))^2}$

Simplify,

$D=\sqrt{((-1)-(1))^2+((4)-(-4))^2}$

$D=\sqrt{(-1-1)^2+(4+4)^2}$

$D=\sqrt{(-2)^2+(8)^2}$

$D=\sqrt{4+64}$

$D=\sqrt{68}$

$D=2\sqrt{17}$