Question

What is the distance between (5, 9), (−7, −7)?

Answer 1

20

Explanation:

Use the distance formula to determine the distance between the two points.

`\text{Distance}=√((x_2=x_1)^2+(y_2-y1)^2)`

Substitute the actual values of the points into the distance formula.

`√(((-7)-5)^2+((-7)-9)^2)`

Simplify.

⇒ Subtract 5 from 7.

`√((-12)^2+((-7)-9)^2)`

⇒ Raise -12 to the power of 2.

`√(144+((-7)-9)^2)`

⇒ Subtract 9 from -7.

`√(144+(-16)^2)`

⇒ Raise -16 to the power of 2.

`√(144+256)`

⇒ Add 144 and 256.

`√(400)`

⇒ Rewrite 400 as 20².

`√(20^2)`

⇒ Pull terms out from under the radical, assuming positive real numbers.

20