ISEE Word Problems Question 208: Answer and Explanation
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Question: 208
1. Point (4, –3) is on a circle with center (–1, 9). What is the diameter of the circle?
- A. 24
- B. 25
- C. 26
- D. 27
Correct Answer: C
Explanation:
The answer is C
First, find the radius by finding the distance from the center to the given point. To do so, use the distance formula, which states that d = 
. Here, d = 
= 
= 13. As the radius is 13, the diameter is 26.
Sketch out the given points and connect them with a line. This line, in addition to being the radius of the circle, is the hypotenuse of a right triangle. Draw in the legs by drawing a vertical line from (4, -3) to (-1, -3) and a horizontal line from (- 1, 9) to (-1, -3). Count the horizontal distance: 5. Count the vertical distance: 12. Use the Pythagorean theorem (or recognize the Pythagorean triple) to find 13 as the radius. Thus, the diameter is 26.