SAT Math Multiple Choice Practice Question 211: Answer and Explanation

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Question: 211

13. On the xy-coordinate plane, what is the area of the circle centered at (-2, 4) with a point on the circle at (1, 0)?

A. 4π
B. 9π
C. 16π
D. 25π
E. 36π

Correct Answer: D


D. You need to figure out what the radius of this circle is. You can use the distance formula on those two points if you can draw a quick sketch of where the points are on the -xy-coordinate plane, like this:

Now you can see that you have a right triangle whose legs are 3 and 4 units long, so the hypotenuse must be 5 units long — it's a 3-4-5 Pythagorean triple! Now that you know that the radius is 5, recall that the formula for the area of a circle is A = πr2, so in this case, the area is π52 = 25π.

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