Question

a circle has a diameter with endpoints (-4, 2) and (2, 10). what is the length of the circles diameter?

Explanation:

Step1: Recall distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(-4,2)\) and \((x_2,y_2)=(2,10)\).

Step2: Substitute values into formula

Substitute \(x_1=-4\), \(y_1 = 2\), \(x_2=2\), \(y_2 = 10\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(2 - (-4))^2+(10 - 2)^2}\\ &=\sqrt{(2 + 4)^2+(8)^2}\\ &=\sqrt{6^2+8^2}\\ &=\sqrt{36 + 64}\\ &=\sqrt{100}\\ & = 10 \end{align*}$$

\]

Answer:

10