Question

the endpoints of a diameter of a circle are $(-4,4)$ and $(5,-4)$. give the radius of the circle. the exact radius is the approximate radius, rounded to 1 decimal place, is question help: video

Explanation:

Step1: Find the distance between the two endpoints (diameter length)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-4,y_1 = 4,x_2=5,y_2=-4\).

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Step2: Calculate the radius

Since \(r=\frac{d}{2}\), and \(d = \sqrt{145}\), then \(r=\frac{\sqrt{145}}{2}\).
For the approximate value, \(\sqrt{145}\approx12.0416\), so \(r=\frac{12.0416}{2}=6.0208\approx6.0\) (rounded to one decimal place)

Answer:

The exact radius is \(\frac{\sqrt{145}}{2}\).
The approximate radius, rounded to 1 decimal place, is \(6.0\).