Question

In circle o, a diameter has endpoints (-5,4) and (3,-6). What is the length of the diameter?

Answer 1

The length of the diameter is 12.81 units.

Step-by-step explanation:

The length of a diameter in a circle can be found using the distance formula. By plugging in the coordinates of the two endpoints of the diameter (-5,4) and (3,-6) into the distance formula, we can calculate the distance between them. The formula for the distance between two points (x1, y1) and (x2, y2) is:

`d = \sqrt{((x2-x1)^2 + (y2-y1)^2)`

Plugging in the values, we get:

`d = \sqrt{((3-(-5))^2 + (-6-4)^2)`

`d = \sqrt{(8^2 + (-10)^2)`

`d = \sqrt{(64 + 100)`

`d = \sqrt{(164)`

d = 12.81

Answer 2

12.8 units (3 s.f.)

Step-by-step explanation:

Distance between 2 points

`= \sqrt{(x1 - x2)^(2) + (y1 - y2)^(2) }`

Thus using the formula above,

length of diameter

`= \sqrt{ {(3 + 5)}^(2) + {( - 6 - 4)}^(2) } \\ = \sqrt{ {8}^(2) + {( - 10)}^(2) } \\ = √(164) \\ = 12.8 \: units \: (3 \: s.f.)`