Question

SOLVE PLEASE! (Help)

Answer 1

1.
`√(218)`

2.
`√(89)`

3.
`2√(17)`

Explanation:

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

`D=√((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=√((x_1-x_2)^2+(y_1-y_2)^2)`

`D=√(((-4)-(3))^2+((6)-(-7))^2)`

Simplify,

`D=√(((-4)-(3))^2+((6)-(-7))^2)`

`D=√((-4-3)^2+(6+7)^2)`

`D=√((-7)^2+(13)^2)`

`D=√(49+169)`

`D=√(218)`

2.

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

Substitute into the formula,

`D=√((x_1-x_2)^2+(y_1-y_2)^2)`

`D=√(((-6)-(2))^2+((-5)-(0))^2)`

Simplify,

`D=√(((-6)-(2))^2+((-5)-(0))^2)`

`D=√((-6-2)^2+(-5-0)^2)`

`D=√((-8)^2+(-5)^2)`

`D=√(64+25)`

`D=√(89)`

3.

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

Substitute into the formula,

`D=√((x_1-x_2)^2+(y_1-y_2)^2)`

`D=√(((-1)-(1))^2+((4)-(-4))^2)`

Simplify,

`D=√(((-1)-(1))^2+((4)-(-4))^2)`

`D=√((-1-1)^2+(4+4)^2)`

`D=√((-2)^2+(8)^2)`

`D=√(4+64)`

`D=√(68)`

`D=2√(17)`