Question

15. What is the area of a circle with a center point of(5,2) and an edge point of (5,7)?

Answer 1

The area, A, of a circle with radius, r, is given by

`A=\pi r^2`

In this case, the radius, r, is the distance between the points (5, 2) and (5, 7).

`\begin{gathered} \text{ Given two points }(x_1,y_1)\text{ and }(x_2,y_2)\text{ on the Cartesian plane, then} \\ \text{the distance betw}een\text{ the points is} \end{gathered}`
`\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Therefore,

`r=\sqrt[]{(5-5)^2+(7-2)^2}=\sqrt[]{0^2+5^2}=\sqrt[]{5^2}=5`

Thus,

`A=\pi(5)^2=25\pi\text{ square units}`