Question

calculate the distance between the points E=(-1,-5) and F=(-8,1) in the coordinate plane. Give an exact answer (not a decimal approximation).

Answer 1

The answer is

`√(85) \: \: \: \: units`

Explanation:

The distance between two points can be found by using the formula

`d = \sqrt{ ({x_1 - x_2})^(2) + ({y_1 - y_2})^(2) } \\`

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

E(-1,-5) and F(-8,1)

The distance between them is

`|EF| = \sqrt{ ({ - 1 + 8})^(2) + ({ - 5 - 1})^(2) } \\ = \sqrt{ {7}^(2) + ({ - 6})^(2) } \\ = √(49 + 36) \: \: \: \: \: \: \: \\ = √(85) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:`

We have the final answer as

`√(85) \: \: \: \: units`

Hope this helps you