Question

Find the distance between the two points in simplest radical form.

(−5,−4) and (−2,−6)

Answer 1

Answer:
`√(13)` units

Work Shown:

`(x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-5-(-2))^2 + (-4-(-6))^2)\\\\d = √((-5+2)^2 + (-4+6)^2)\\\\d = √((-3)^2 + (2)^2)\\\\d = √(9 + 4)\\\\d = √(13)\\\\d \approx 3.6056\\\\`

I used the distance formula.

A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).