Question

the endpoints of a diameter of a circle are $(-2,7)$ and $(5,3)$. give the radius of the circle. the exact radius is the approximate radius, rounded to 1 decimal place, is question help: video check answer

Explanation:

Step1: Find the length of the diameter using the distance formula

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, \(x_1=-2,y_1 = 7,x_2=5,y_2 = 3\).
\(d=\sqrt{(5-(-2))^2+(3 - 7)^2}=\sqrt{(5 + 2)^2+(-4)^2}=\sqrt{7^2+(-4)^2}=\sqrt{49 + 16}=\sqrt{65}\)

Step2: Calculate the radius

Since the radius \(r=\frac{d}{2}\), and \(d = \sqrt{65}\), then \(r=\frac{\sqrt{65}}{2}\).
For the approximate value, \(\sqrt{65}\approx8.062\), so \(r=\frac{8.062}{2}=4.031\approx4.0\) (rounded to one decimal place)

Answer:

The exact radius is \(\frac{\sqrt{65}}{2}\)
The approximate radius, rounded to 1 decimal place, is \(4.0\)