Question 1 Explanation_Digital SAT Math Practice Test 5

Student-produced response directions

If you find more than one correct answer, enter only one answer.

You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.

If your answer is a fraction that doesn't fit in the provided space, enter the decimal equivalent.

If your answer is a decimal that doesn't fit in the provided space, enter it by truncating or rounding at the fourth digit.

If your answer is a mixed number (such as

3 \frac{1}{2}

), enter it as an improper fraction (7/2) or its decimal equivalent (3.5).

Don't enter symbols such as a percent sign, comma, or dollar sign.

Example

Answer	Acceptable ways to enter answer	Unacceptable: will NOT receive credit
3.5	3.5 3.50 7/2	31/2 3 1/2
$\frac{2}{3}$	2/3 .6666 .6667 0.666 0.667	0.66 .66 0.67 .67
$- \frac{1}{3}$	-1/3 -.3333 -0.333	-.33 -0.33

Mark for Review

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?

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Correct Answer:

Your Answer:

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.