SAT Mathematics Practice Test 7

Question : 49 of 59

Marks: +1, -0

A circle in the xy‑plane has equation

(x + 3)^2 + (y − 1)^2 = 25

. Which of the following points does NOT lie in the interior of the circle?

(-7, 3)
(-3, 1)
(0, 0)
(3, 2)

Validate

Solution:

The circle with equation

(x + 3)^2 + (y – 1)^2 = 25

has center (–3, 1) and radius 5. For a point to be inside of the circle, the distance from that point to the center must be less than the radius, 5. The distance between (3, 2) and (–3, 1) is

√{(-3 -3)^2 + (1 - 2)^2} = √{(-6)^2 + (-1)^2} = √37

, which is greater than 5. Therefore, (3, 2) doesNOT lie in the interior of the circle.

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