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# Coordinates

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The points (-3,2) and (-2,-2) lie on a circle whose center is on the x-axis. What is the radius of the circle?

Dec 14, 2021

#1
+203
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With on the circle do you mean on the circumference of the circle or inside the circle?

Just a guess: 0.5

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Dec 14, 2021
edited by AlgebraGuru  Dec 14, 2021
#2
+13716
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What is the radius of the circle?

HelloGuest!

The middle of the points (-3,2) and (-2, -2) is the point (-2.5,0). The vertical has a gradient of m = 1/4.

$$y=m(x-x_1)+y_1\\ y=0.25(x+2.5)+0\\ y=0.25x+0.625\ |\ \color{blue}x_c=0 \\ \color{blue}y_c=0.625$$

$$r^2=(2-0.625)^2+|-3\ |^2\\ r=\sqrt{10.891}$$

$$r=3.3$$

$$The\ radius\ of\ the\ circle\ is\ {\color{blue}3.3}\ .$$

!

Dec 14, 2021
edited by asinus  Dec 14, 2021