Problem Solving

BTGmoderatorLU wrote:Source: Veritas Prep



Which of the following is NOT a point on the circle of radius 5 and center O as graphed above?

A. (-1, 2)
B. (8, -1)
C. (0, -5)
D. (6, 3)
E. (7, -6)

The OA is E.

Distance formula:

Note that distance between two points whose coordinates are (x, y) and (a, b) is given by

= √[(x - a)^2 + (y - b)^2]

The point whose coordinates are (x, y) is on the circle and the point whose coordinates are (a, b) is the center of the circle, thus, a = 3 and b = - 1.

Thus, Radius = √[(x - a)^2 + (y - b)^2] = √[(x - 3)^2 + (y + 1)^2]

5 = √[(x - 3)^2 + (y + 1)^2]

25 = (x - 3)^2 + (y + 1)^2

You may lug-in option values and check which one fits. You'll find that option E: (7, -6) is NOT on the circle.

Let's see:

Option E: (7, -6)

(7 - 3)^2 + (-6 + 1)^2 = 16 + 25 = 41 ≠ 25.

The correct answer: E

Hope this helps!

-Jay
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