Possible coordinates on a circle (SAT). Game on.

Possible coordinates on a circle (SAT) is a grade 10 math skill aligned to Common Core standard HSG.GPE.B.4. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 possible coordinates on a circle (sat) problems our math games drill.

CCSS HSG.GPE.B.410 questions in the bank
Kickoff

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Warm-upeasy

The graph of the equation (x7)2+(y3)2=25(x - 7)^2 + (y - 3)^2 = 25 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for a?a\textsf{?}

The center is (7,3)(7, 3) and the radius is 5.5\textsf{.} A point on the circle must satisfy 75a7+5,7 - 5 \le a \le 7 + 5\textsf{,} so 2a12.2 \le a \le 12\textsf{.} The value 99 is in this interval.

Mid-gameeasy

The graph of the equation (x4)2+(y+5)2=36(x - 4)^2 + (y + 5)^2 = 36 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for a?a\textsf{?}

The center is (4,5)(4, -5) and the radius is 6.6\textsf{.} A point on the circle must satisfy 46a4+6,4 - 6 \le a \le 4 + 6\textsf{,} so 2a10.-2 \le a \le 10\textsf{.} The value 33 is in this interval.

Mid-gameeasy

The graph of the equation (x9)2+(y2)2=64(x - 9)^2 + (y - 2)^2 = 64 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for b?b\textsf{?}

The center is (9,2)(9, 2) and the radius is 8.8\textsf{.} A point on the circle must satisfy 28b2+8,2 - 8 \le b \le 2 + 8\textsf{,} so 6b10.-6 \le b \le 10\textsf{.} The value 44 is in this interval.

Mid-gamemedium

The graph of the equation (x+6)2+(y4)2=100(x + 6)^2 + (y - 4)^2 = 100 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for a?a\textsf{?}

The center is (6,4)(-6, 4) and the radius is 10.10\textsf{.} A point on the circle must satisfy 610a6+10,-6 - 10 \le a \le -6 + 10\textsf{,} so 16a4.-16 \le a \le 4\textsf{.} The value 11-11 is in this interval.

Mid-gamemedium

The graph of the equation (x2)2+(y8)2=81(x - 2)^2 + (y - 8)^2 = 81 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for a?a\textsf{?}

The center is (2,8)(2, 8) and the radius is 9.9\textsf{.} A point on the circle must satisfy 29a2+9,2 - 9 \le a \le 2 + 9\textsf{,} so 7a11.-7 \le a \le 11\textsf{.} The value 55 is in this interval.

Mid-gamemedium

The graph of the equation (x+1)2+(y+10)2=144(x + 1)^2 + (y + 10)^2 = 144 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for a?a\textsf{?}

The center is (1,10)(-1, -10) and the radius is 12.12\textsf{.} A point on the circle must satisfy 112a1+12,-1 - 12 \le a \le -1 + 12\textsf{,} so 13a11.-13 \le a \le 11\textsf{.} The value 66 is in this interval.

Mid-gamemedium

The graph of the equation (x+8)2+(y6)2=169(x + 8)^2 + (y - 6)^2 = 169 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for b?b\textsf{?}

The center is (8,6)(-8, 6) and the radius is 13.13\textsf{.} A point on the circle must satisfy 613b6+13,6 - 13 \le b \le 6 + 13\textsf{,} so 7b19.-7 \le b \le 19\textsf{.} The value 1111 is in this interval.

Buzzer beatermedium

The graph of the equation (x+2)2+(y15)2=196(x + 2)^2 + (y - 15)^2 = 196 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for a?a\textsf{?}

The center is (2,15)(-2, 15) and the radius is 14.14\textsf{.} A point on the circle must satisfy 214a2+14,-2 - 14 \le a \le -2 + 14\textsf{,} so 16a12.-16 \le a \le 12\textsf{.} The value 5-5 is in this interval.

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

Drill it inside a game.

The free placement test finds your level, then every match serves possible coordinates on a circle (sat) questions at exactly the right difficulty.