Question

DRAFTING The design for a park is drawn on a coordinate graph. The perimeter of the park is modeled by the equation ( x - 3 ) 2 + ( y - 7 ) 2 = 225 . Each unit on the graph represents 10 feet. What is the center and radius of the actual park?

Answer 1

Geometry - Circle

The perimeter of the park is modelled by

$\quad (x-3)^{2}+(y-7)^{2}=225$

$\Rightarrow (x-3)^{2}+(y-7)^{2}=15^{2}$

So the centre of the circle is at $(3,\:7)$ and its radius is $15$ units.

Given, each unit on the graph represents $10$ feet.

So, $(3,\:7)\Rightarrow (30,\:70)$

and $15$ units $\Rightarrow 150$ feet

Answer: The center and radius of the actual park are at $\color{blue}{(30,\:70)}$ and is $\color{blue}{150}$ feet respectively.