Coordinate Geometry practice questions

Coordinate Geometry questions

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1. 1Coordinate geometryFoundation

   What is the distance between (-1, 2) and (3, 2) on a coordinate plane?What is the distance between (-1, 2) and (3, 2) on a coordinate plane?

   • A22
   • B55
   • C44
   • D88
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   Answer: 44

   The points have the same y-coordinate, so the horizontal distance is 3 - (-1) = 4.The points have the same y-coordinate, so the horizontal distance is 3 - (-1) = 4.

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2. 2Coordinate geometryFoundation

   Enter the distance between the points (0, 0) and (6, 8).Enter the distance between the points (0, 0) and (6, 8).

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 1010

   The distance is the square root of 6² + 8² = 36 + 64 = 100, which is 10.The distance is the square root of 6^2 + 8^2 = 36 + 64 = 100, which is 10.

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3. 3Coordinate geometryStandard

   What is the midpoint of the segment joining (2, -1) and (8, 5)?What is the midpoint of the segment joining (2, -1) and (8, 5)?

   • A(3, 3)(3, 3)
   • B(5, 2)(5, 2)
   • C(6, 6)(6, 6)
   • D(10, 4)(10, 4)
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   Answer: (5, 2)(5, 2)

   Average each coordinate: x is 2 + 82 = 5 and y is -1 + 52 = 2.Average each coordinate: x is (2 + 8)/2 = 5 and y is (-1 + 5)/2 = 2.

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4. 4Coordinate geometryStandard

   A circle has center (3, -1) and passes through (3, 4). What is its radius?A circle has center (3, -1) and passes through (3, 4). What is its radius?

   • A√10√(10)
   • B55
   • C33
   • D44
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   Answer: 55

   The two points share an x-coordinate, so the distance between them is the difference in y: 4 - (-1) = 5. No distance formula is needed.The two points share an x-coordinate, so the distance between them is the difference in y: 4 - (-1) = 5. No distance formula is needed.

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5. 5Coordinate geometryStandard

   A line segment has one endpoint at (1, 2) and midpoint at (4, 6). What is the other endpoint?A line segment has one endpoint at (1, 2) and midpoint at (4, 6). What is the other endpoint?

   • A(5, 8)(5, 8)
   • B(3, 4)(3, 4)
   • C(2.5, 4)(2.5, 4)
   • D(7, 10)(7, 10)
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   Answer: (7, 10)(7, 10)

   The midpoint is the average of the endpoints, so the other endpoint is twice the midpoint minus the known one: (8 - 1, 12 - 2) = (7, 10).The midpoint is the average of the endpoints, so the other endpoint is twice the midpoint minus the known one: (8 - 1, 12 - 2) = (7, 10).

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6. 6Coordinate geometryStandard

   What is the slope of a line perpendicular to the segment joining (1, 3) and (5, 11)?What is the slope of a line perpendicular to the segment joining (1, 3) and (5, 11)?

   • A-2-2
   • B-12-1/2
   • C22
   • D121/2
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   Answer: -12-1/2

   The segment's slope is 11 - 35 - 1 = 2. A perpendicular slope is the negative reciprocal, which is -12.The segment's slope is (11 - 3)/(5 - 1) = 2. A perpendicular slope is the negative reciprocal, which is -1/2.

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7. 7Coordinate geometryStandard

   Which point lies on the line y = 2x - 5?Which point lies on the line y = 2x - 5?

   • A(2, 1)(2, 1)
   • B(4, 3)(4, 3)
   • C(3, 4)(3, 4)
   • D(0, 5)(0, 5)
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   Answer: (4, 3)(4, 3)

   Substituting x = 4 gives y = 8 - 5 = 3, so (4, 3) is on the line. Checking (2, 1) gives y = -1, not 1.Substituting x = 4 gives y = 8 - 5 = 3, so (4, 3) is on the line. Checking (2, 1) gives y = -1, not 1.

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8. 8Coordinate geometryStandard

   What is the distance between the points (-3, 2) and (5, 8)?What is the distance between the points (-3, 2) and (5, 8)?

   • A1414
   • Bthe square root of 68the square root of 68
   • C88
   • D1010
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   Answer: 1010

   The horizontal gap is 8 and the vertical gap is 6, so the distance is the square root of 64 + 36 = 100, which is 10. Adding the gaps gives 14, and subtracting the coordinates in the wrong order before squaring is what produces the square root of 68.The horizontal gap is 8 and the vertical gap is 6, so the distance is the square root of 64 + 36 = 100, which is 10. Adding the gaps gives 14, and subtracting the coordinates in the wrong order before squaring is what produces the square root of 68.

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9. 9Coordinate geometryStandard

   What is the slope of the line through (-2, -5) and (4, 7)?What is the slope of the line through (-2, -5) and (4, 7)?

   • A121/2
   • B-2-2
   • C66
   • D22
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   Answer: 22

   The change in y is 7 - (-5) = 12 and the change in x is 4 - (-2) = 6, so the slope is 126 = 2. Both subtractions involve a double negative, which is where the sign errors come from.The change in y is 7 - (-5) = 12 and the change in x is 4 - (-2) = 6, so the slope is 12/6 = 2. Both subtractions involve a double negative, which is where the sign errors come from.

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10. 10Coordinate geometryStandard

    What is the midpoint of the segment joining (3, -7) and (11, 1)?What is the midpoint of the segment joining (3, -7) and (11, 1)?

    • A(7, -3)(7, -3)
    • B(8, -6)(8, -6)
    • C(14, -6)(14, -6)
    • D(4, -4)(4, -4)
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    Answer: (7, -3)(7, -3)

    Average each coordinate: 3 + 112 = 7 and -7 + 12 = -3. Adding without halving gives (14, -6), and halving the differences instead gives a displacement rather than a point.Average each coordinate: (3 + 11)/2 = 7 and (-7 + 1)/2 = -3. Adding without halving gives (14, -6), and halving the differences instead gives a displacement rather than a point.

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11. 11Coordinate geometryStandard

    What is the midpoint of the segment joining (-6, 3) and (2, 11)?What is the midpoint of the segment joining (-6, 3) and (2, 11)?

    • A(-2, 7)(-2, 7)
    • B(-4, 14)(-4, 14)
    • C(4, -4)(4, -4)
    • D(-8, -8)(-8, -8)
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    Answer: (-2, 7)(-2, 7)

    Average each coordinate: -6 + 22 = -2 and 3 + 112 = 7. Adding without halving gives (-4, 14).Average each coordinate: (-6 + 2)/2 = -2 and (3 + 11)/2 = 7. Adding without halving gives (-4, 14).

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12. 12Coordinate geometryChallenge

    What is the midpoint of the segment joining (-5, 8) and (3, -2)?What is the midpoint of the segment joining (-5, 8) and (3, -2)?

    • A(-4, 5)(-4, 5)
    • B(-2, 6)(-2, 6)
    • C(4, -5)(4, -5)
    • D(-1, 3)(-1, 3)
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    Answer: (-1, 3)(-1, 3)

    A midpoint averages each coordinate separately: -5 + 32 = -1 and 8 + (-2)2 = 3. The choice (-2, 6) adds the coordinates without halving them, and (4, -5) halves the differences instead, which gives a displacement rather than a point.A midpoint averages each coordinate separately: (-5 + 3)/2 = -1 and (8 + (-2))/2 = 3. The choice (-2, 6) adds the coordinates without halving them, and (4, -5) halves the differences instead, which gives a displacement rather than a point.

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13. 13Coordinate geometryChallenge

    A line passes through (2, 3) and is perpendicular to the line y = -(14)x + 7. What is its slope?A line passes through (2, 3) and is perpendicular to the line y = -(1/4)x + 7. What is its slope?

    • A-14-1/4
    • B-4-4
    • C141/4
    • D44
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    Answer: 44

    Perpendicular slopes are negative reciprocals: the negative reciprocal of -14 is 4. Taking only the reciprocal gives -4 and only the negative gives 14; the point (2, 3) fixes the intercept, not the slope.Perpendicular slopes are negative reciprocals: the negative reciprocal of -1/4 is 4. Taking only the reciprocal gives -4 and only the negative gives 1/4; the point (2, 3) fixes the intercept, not the slope.

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