PSAT Math Grid-Ins Question 132: Answer and Explanation
Question: 132
If a circle has the equation (x - 4)2 + (y - 3)2 = 36, what is the shortest straight-line distance from the center of the circle to the origin?
Correct Answer: 5
Explanation:
5 Based on the general equation of a circle, (x - h)2 + (y - k)2 = r2, the center point is (h, k). For this circle, the center point is (4, 3). This point is a distance of 5 from the origin, which has thecoordinates (0, 0). The graph of the circle is as follows:
You can calculate the shortest straight-line distance by using the distance formula or, even easier, recognizing that these numbers form a Pythagorean triple: 3-4-5. Recognizing that this is a Pythagorean triple will save you the time and trouble of calculating the distance using the distance formula.
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