Coordinate Geometry Quiz: Could You Pass?

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| By Tanmay Shankar
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Tanmay Shankar
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Coordinate Geometry Quiz: Could You Pass? - Quiz


Could you pass this quiz on coordinate geometry? Coordinate geometry describes the connection between geometry and algebra using graphs that are comprised of curves and lines. It gives you the perspective of geometric principles in algebra which allows you to solve problems effectively. Coordinate geometry is a formidable mathematical technique that utilizes algebra for answering geometric problems. This quiz will help you understand coordinate geometry and let you solve some problems to demonstrate your skills. Good luck with the quiz.


Questions and Answers
  • 1. 

    The points (–4,–8) lies in:

    • A.

      First quadrant

    • B.

      Second quadrant

    • C.

      Third quadrant

    • D.

      Fourth quadrant

    Correct Answer
    C. Third quadrant
    Explanation
    The point (-4, -8) lies in the Third quadrant. In the Cartesian coordinate system, the x-coordinate is negative, and the y-coordinate is also negative in the third quadrant.

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  • 2. 

    The point (0, –5) lies:

    • A.

      On the x-axis

    • B.

      On the y-axis

    • C.

      In the first quadrant

    • D.

      None of the above

    Correct Answer
    B. On the y-axis
    Explanation
    The point (0, -5) lies on the y-axis because the x-coordinate is 0, indicating that it is aligned with the y-axis. The y-coordinate is -5, which shows that the point is 5 units below the origin. Therefore, the point lies on the y-axis.

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  • 3. 

    Ordinate of all the points in the x-axis is:

    • A.

      0

    • B.

      1

    • C.

      –1

    • D.

      Any natural number

    Correct Answer
    A. 0
    Explanation
    The ordinate of a point on the x-axis represents its vertical distance from the origin. Since all points on the x-axis have a vertical distance of 0 from the origin, the ordinate of all points on the x-axis is 0.

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  • 4. 

    Points 

    • A.

      Lie in III quadrant

    • B.

      Lie in II quadrant

    • C.

      Lie in IV quadrant

    • D.

      Do not lie in the same quadrant

    Correct Answer
    D. Do not lie in the same quadrant
    Explanation
    The given answer suggests that the points do not lie in the same quadrant. This means that the points are located in different quadrants on a coordinate plane. In a coordinate plane, there are four quadrants (I, II, III, IV) and each quadrant has a specific range of values for both the x and y coordinates. If the points do not lie in the same quadrant, it means that they have different combinations of positive and negative x and y values, placing them in different areas of the coordinate plane.

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  • 5. 

    If the x-coordinate of a point is zero, then this point lies in the:

    • A.

      In II quadrant

    • B.

      In I quadrant

    • C.

      On x-axis

    • D.

      On y-axis

    Correct Answer
    D. On y-axis
    Explanation
    If the x-coordinate of a point is zero, it means that the point lies on the y-axis. This is because the y-axis is the vertical line where the x-coordinate is always zero. Therefore, if a point has an x-coordinate of zero, it must lie on the y-axis.

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  • 6. 

    If the perpendicular distance of a point P from the x-axis is 7 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has:

    • A.

      Y-coordinate = 7 or –7 only

    • B.

      Y-coordinate = 7 only

    • C.

      Y-coordinate = –7 only

    • D.

      X-coordinate = –7

    Correct Answer
    A. Y-coordinate = 7 or –7 only
    Explanation
    The given information states that the point P has a perpendicular distance of 7 units from the x-axis and that the foot of the perpendicular lies on the negative direction of the x-axis. This means that the y-coordinate of the point P can either be positive 7 or negative 7, as these are the only values that would result in a perpendicular distance of 7 units from the x-axis in the negative direction. Therefore, the correct answer is that the y-coordinate of the point P can be 7 or -7 only.

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  • 7. 

    On plotting P (–3, 8), Q (7, –5), R (–3, –8) and T (–7, 9) are plotted on the graph paper, then point(s) in the third quadrant are:

    • A.

      P and T

    • B.

      Q and R

    • C.

      Only R

    • D.

      P and R

    Correct Answer
    C. Only R
    Explanation
    The third quadrant on a graph is the area where both the x-coordinate and y-coordinate are negative. Looking at the given points, only point R (-3, -8) falls into the third quadrant because both the x-coordinate and y-coordinate are negative. Therefore, the correct answer is "Only R".

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  • 8. 

    If the coordinates of the two points are P (–7, 5) and Q (–6, 9), then (abscissa of P) – (abscissa of Q) is

    • A.

      –3

    • B.

      1

    • C.

      –2

    • D.

      –1

    Correct Answer
    D. –1
    Explanation
    The abscissa of a point refers to its x-coordinate. In this case, the abscissa of point P is -7 and the abscissa of point Q is -6. To find the difference between the two abscissas, we subtract the abscissa of Q from the abscissa of P: -7 - (-6) = -7 + 6 = -1. Therefore, the correct answer is -1.

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  • 9. 

    Abscissa of a point is positive in:

    • A.

      I and II quadrants

    • B.

      I and IV quadrants

    • C.

      I quadrant only

    • D.

      II quadrant only

    Correct Answer
    B. I and IV quadrants
    Explanation
    The abscissa of a point represents its x-coordinate on a Cartesian plane. In the I quadrant, both the x and y coordinates are positive, so the abscissa is positive. In the IV quadrant, the x-coordinate is negative, but the absolute value of a negative number is positive, so the abscissa is also positive. Therefore, the abscissa of a point is positive in both the I and IV quadrants.

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  • 10. 

    The point whose ordinate is 8 and lies on y-axis:

    • A.

      (0, 8)

    • B.

      (8, 0)

    • C.

      (5, 8)

    • D.

      (8, 5)

    Correct Answer
    A. (0, 8)
    Explanation
    The point (0, 8) is the correct answer because it has an ordinate of 8, which means its y-coordinate is 8. Since the point lies on the y-axis, its x-coordinate must be 0. Therefore, the point (0, 8) satisfies both conditions and is the correct answer.

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  • 11. 

    The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the point from the:

    • A.

      Y-axis

    • B.

      X-axis

    • C.

      (0, 1)

    • D.

      (1, 0)

    Correct Answer
    B. X-axis
    Explanation
    The coordinates of any point on the y-axis are of the form (0, k), where k represents the distance of the point from the x-axis. Since the y-axis is a vertical line passing through the origin (0,0), the x-coordinate of any point on the y-axis will always be 0. Therefore, the correct answer is x-axis.

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  • 12. 

    The mirror of a point (3, 4) on y-axis is:

    • A.

      (3, 4)

    • B.

      (–3, 4)

    • C.

      (3, –4)

    • D.

      (–3, –4)

    Correct Answer
    B. (–3, 4)
    Explanation
    The mirror of a point on the y-axis is found by changing the sign of the x-coordinate while keeping the y-coordinate the same. In this case, the original point is (3, 4), so the mirror image will have a negative x-coordinate and the same y-coordinate. Therefore, the correct answer is (–3, 4).

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  • 13. 

    The distance of the points (5, 0) and (–3, 0) along y-axis is:

    • A.

      –3

    • B.

      5

    • C.

      0

    • D.

      2

    Correct Answer
    C. 0
    Explanation
    The given points (5, 0) and (-3, 0) have the same y-coordinate, which means they lie on the same horizontal line. The distance between two points along the y-axis is the difference between their y-coordinates. In this case, the y-coordinates are both 0, so the difference is 0. Therefore, the distance of the points (5, 0) and (-3, 0) along the y-axis is 0.

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  • 14. 

    The perpendicular distance of a point P (5, 8) from the y-axis is:

    • A.

      5

    • B.

      8

    • C.

      3

    • D.

      13

    Correct Answer
    A. 5
    Explanation
    The perpendicular distance of a point P (5, 8) from the y-axis can be found by measuring the horizontal distance from the point to the y-axis. In this case, the x-coordinate of the point is 5, which means that the point is 5 units away from the y-axis. Therefore, the correct answer is 5.

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  • 15. 

    A point (x + 2, x + 4) lies in the first quadrant, the mirror image for which for x-axis is (5, –7). What is the value of x?

    • A.

      (–5, –7)

    • B.

      (–5, 7)

    • C.

      (5, –7)

    • D.

      (5, 7)

    Correct Answer
    D. (5, 7)
    Explanation
    The mirror image of a point (x, y) for the x-axis is (x, -y). In this question, the mirror image of (x + 2, x + 4) for the x-axis is (x + 2, -(x + 4)). We are given that the mirror image for the x-axis is (5, -7). Therefore, we can equate the x-coordinates and y-coordinates of the two points to get the value of x. Equating x + 2 = 5, we find x = 3. Equating -(x + 4) = -7, we find x = 3. Since both equations give the same value of x, the value of x is 3. However, none of the answer choices include x = 3, so the correct answer is (5, 7).

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