Coordinate Geometry

Geometry Level pending

A circle has a diameter AB where A is the point (1,1) and B is the point (7,9). Find the radius of the circle (in units).


The answer is 5.

Sheryl-Lynn Tan by Sheryl-Lynn Tan , 18, Singapore

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1 solution

We can use the distance formula to solve for the length of the diameter. We have

d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = ( 7 − 1 ) 2 + ( 9 − 1 ) 2 = 6 2 + 8 2 = 36 + 64 = 100 = 10 d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(7-1)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10

Since the radius is twice the diameter, we have

r = d 2 = 10 2 = r=\dfrac{d}{2}=\dfrac{10}{2}= 5 \boxed{5}

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