Question

The point (5,4) lies on a circle. What is the length of the radius of this circle if the center is located at (3,2)? I need numbers. Please!

Answer 1

Answer:

r = 2√2

Step-by-step explanation:

A( $x_{1}$ , $y_{1}$ )  , B ( $x_{2}$ , $y_{2}$ )

AB = √[($x_{1}$ - $x_{2}$)² + ($y_{1}$ - $y_{2}$)²]

~~~~~~~

r = $\sqrt{(5-3)^2+(4-2)^2}$ = √8 = 2√2  

Answer 2

Given:

A point on circle=(5, 4)

Center=(3, 2)

To find:

The radius

Solution:

The required length of the circle's radius is 2√2 units.

We can obtain the radius by using the following formula-

Let the radius be r.

$(x-h)^{2} +(y-k)^{2} =r^{2}$

Here, (x, y) refers to a point lying on the given circle, (h, k) is the centre's coordinates and r is the radius.

Using the values, we will calculate the radius.

$(5-3)^{2} +(4-2)^{2} =r^{2}$

$2^{2} +2^{2} =r^{2}$

4+4=$r^{2}$

8=$r^{2}$

√8=r

2√2=r

So, the radius=2√2 units.

Therefore, the required length of the circle's radius is 2√2 units.