Question

A circle has its origin at (0, 0). The point (5, 7) is on the edge of the circle. What is the radius of the circle?

Select one:
A. r = 6√2
B. r = 2√18
C. r = 4√21
D. r = √74
E. There is not enough information to answer this question.

Answer 1

The radius of the circle is √74

Explanation:

Radius of a circle is the distance between the centre of a circle and its circumference.

The origin of the circle (0,0) will be its centre.

The point on the edge of the circle is the point on its circumference which is (5,7).

The radius of the circle will be the distance between this two points according to definition.

R = √(x2-x1)²+(y2-y1)²

Given (x1, y1) = (0,0) and (x2, y2) = (5, 7)

x1 = 0, y1 = 0, x2 = 5, y2 = 7

Substituting into the formula we have;

R = √(5-0)²+(7-0)²

R = √5²+7²

R = √25+49

R = √74

Answer 2

Explanation:

Given that a centre has an origin (0,0) and (5,7) at the edge.

What is the radius of the circle

This is a direct question, we can apply coordinate geometry by finding the distance between two point, .

From co-ordinate geometry, the distance between two points is

d =√[(x2-x1)² + (y2-y1)²]

So, applying this

Point 1 = (x1,y1) = (0,0)

Point 2 = (x2,y2) = (5,7)

The radius of the is

r = √[(x2-x1)² + (y2-y1)²]

r = √[(5-0)² + (7-0)²]

r = √[5² + 7²]

r = √(25 + 49)

r = √74

The correct answer is D

D. √74