Digital PSAT Math Practice Question 323: Answer and Explanation

Question: 323

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?

Grid-In:

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 the coordinates (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.