Question

If the endpoints of the diameter of a circle are (3, 5) and (-1, -3), find the radius of the cirlcle.

• A. $4\sqrt{5}$ units
• B. $\sqrt{5}$ units
• C. $2\sqrt{5}$ units
• D. $5\sqrt{5}$ units

Answer 1

The correct option is C $2\sqrt{5}$ units

Given: Endpoints of the diameter are (3, 5) and (-1, -3).

The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}.$

So, diameter = $\sqrt{(-1-3{)}^2+(-3-5{)}^2}$

Diameter = $\sqrt{(-4{)}^2+(-8{)}^2}$

Diameter = $\sqrt{16+64}$

Diameter = $\sqrt{80}$

Diameter = $4\sqrt{5}$ units
Hence, radius = $2\sqrt{5}$ units