Question

question 9 of 10
the end - points of the diameter of a circle are at the points a(3,5) and b(5,6). what is the length of the radius? (give your answer correct to 2 decimal places if necessary)

Explanation:

Step1: Use distance formula for diameter

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 3,y_1 = 5,x_2 = 5,y_2 = 6$. So $d=\sqrt{(5 - 3)^2+(6 - 5)^2}$.

Step2: Calculate value of diameter

$d=\sqrt{2^2+1^2}=\sqrt{4 + 1}=\sqrt{5}$.

Step3: Find radius

Since the radius $r=\frac{d}{2}$, and $d = \sqrt{5}$, then $r=\frac{\sqrt{5}}{2}\approx1.12$.

Answer:

$1.12$