+0  
 
0
82
2
avatar

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

 Apr 14, 2022

Best Answer 

 #1
avatar+2444 
+1

Because of the shape of a circle, both the points have to be the same distance from the center. 

 

Using the Pythagorean theorem, we can write this as an equation: \(\sqrt{(2-x)^2 + (3-y)^2} = \sqrt{(3-x)^2+(2-y)^2}\)

 

Substituting 0 for y, we get: \((2-x)^2 +9 = (3-x)^2+4\)

 

Solving, we find \(x = 0\), meaning the coordinates of the center are: \((0, 0)\)

 

Using the Pythagorean Theorem, we find that the radius of the circle is \(\color{brown}\boxed{\sqrt{13}}\)

 Apr 14, 2022
 #1
avatar+2444 
+1
Best Answer

Because of the shape of a circle, both the points have to be the same distance from the center. 

 

Using the Pythagorean theorem, we can write this as an equation: \(\sqrt{(2-x)^2 + (3-y)^2} = \sqrt{(3-x)^2+(2-y)^2}\)

 

Substituting 0 for y, we get: \((2-x)^2 +9 = (3-x)^2+4\)

 

Solving, we find \(x = 0\), meaning the coordinates of the center are: \((0, 0)\)

 

Using the Pythagorean Theorem, we find that the radius of the circle is \(\color{brown}\boxed{\sqrt{13}}\)

BuilderBoi Apr 14, 2022
 #2
avatar+115 
-3

Good BØ¥¥¥¥

Kakashi  Apr 14, 2022

14 Online Users