Question

What is the distance between centers of two circles given the centers are (5, -4) and (-4, 2)?

Round to the nearest tenth.​

Answer 1

10.8 units.

Explanation:

Given:

Centers of two circles are
`(5,-4)` and
`(-4,2)`.

Distance between two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given as:

Distance,
`D=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

Here,
`(x_(1),y_(1))` is
`(5,-4)` and
`(x_(2),y_(2))` is
`(-4,2)`.

Plug in these values and calculate the distance between these 2 points.

Distance between the centers is given as:

`D=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}\\ D=\sqrt{(-4-5)^(2)+(2-(-4))^(2)}\\ D=\sqrt{(-9)^(2)+(6)^(2)}\\ D=√(81+36)\\ D=√(117)=10.8`

Therefore, the distance between the centers of the two circles is 10.8 units.