Question

Find the distance between the points (0-4) and (-6,7)

Answer 1

`\huge{\boxed{√(157) \approx 12.5299641}}`

The distance formula is
`√((x_2-x_1)^2+(y_2-y_1)^2)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are the points.

Substitute in the values.
`√((-6-0)^2+(7-(-4))^2)`

Simplify the negative subtraction.
`√((-6-0)^2+(7+4)^2)`

Subtract and add.
`√((-6)^2+11^2)`

Solve the exponents.
`√(36+121)`

Add.
`\boxed{√(157)}`

You can approximate this value using a calculator.
`√(157) \approx \boxed{12.5299641}`

Answer 2

`\large\boxed{√(157)\approx12.5}`

Explanation:

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have the points (0, -4) and (-6, 7).

Substitute:

`d=√((-6-0)^2+(7-(-4))^2)=√((-6)^2+11^2)=√(36+121)=√(157)`