Coordinate Geometry

12 Grade 9 Mathematics questions on Coordinate Geometry, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   4 marks

   The vertices of a triangle are A(0, 0), B(6, 0), and C(3, 4). Find the perimeter of the triangle.

   (4 marks)

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2. Question 2

   1 mark

   The distance between (0, 0) and (3, 4) is ___

   A. 7

   B. 5

   C. 3

   D. 4

   (1 mark)

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3. Question 3

   3 marks

   Plot and label the points A(2, 3), B(−1, 4), and C(0, −2) on a Cartesian plane. State the quadrant (or axis) each point is in.

   (3 marks)

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4. Question 4

   1 mark

   The midpoint of (2, 4) and (6, 8) is ___

   A. (3, 4)

   B. (8, 12)

   C. (2, 2)

   D. (4, 6)

   (1 mark)

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5. Question 5

   1 mark

   Find the length of the line segment joining $A(1,2)$ and $B(4,6)$.

   A. $25$

   B. $5$

   C. $\sqrt{7}$

   D. $7$

   (1 mark)

   Marking scheme

   B. $5$ — the distance formula is Pythagoras in disguise: $\sqrt{(4-1{)}^2+(6-2{)}^2}=\sqrt{9+16}=\sqrt{25}=5$. A is $25$, the answer before taking the square root.

6. Question 6

   4 marks

   Find the length and midpoint of the line segment joining P(−2, 1) and Q(4, 9).

   (4 marks)

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7. Question 7

   1 mark

   The gradient of the line joining (0, 0) to (4, 8) is ___

   A. 2

   B. 8

   C. 4

   D. 0.5

   (1 mark)

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8. Question 8

   1 mark

   Which quadrant contains the point (−2, 5)?

   A. Fourth quadrant

   B. Third quadrant

   C. Second quadrant

   D. First quadrant

   (1 mark)

   Marking scheme

   C. Second quadrant — $x$ is negative and $y$ positive. The quadrants are numbered anticlockwise from the top right, so the pair of signs fixes the quadrant: $(+,+)$ first, $(-,+)$ second, $(-,-)$ third, $(+,-)$ fourth.

9. Question 9

   1 mark

   Find the midpoint of the line segment joining $A(-3,5)$ and $B(7,-1)$.

   A. $(5,-3)$

   B. $(2,2)$

   C. $(4,4)$

   D. $(-2,2)$

   (1 mark)

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10. Question 10

    1 mark

    What are the coordinates of the origin?

    A. (0, 0)

    B. (1, 0)

    C. (1, 1)

    D. (0, 1)

    (1 mark)

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11. Question 11

    1 mark

    A point in the third quadrant has coordinates ___

    A. (−3, −4)

    B. (3, −4)

    C. (−3, 4)

    D. (3, 4)

    (1 mark)

    Marking scheme

    A. $(-3,-4)$ — the third quadrant is where both coordinates are negative. The quadrants are numbered anticlockwise from the top right, so the pair of signs fixes the quadrant: $(+,+)$ first, $(-,+)$ second, $(-,-)$ third, $(+,-)$ fourth.

12. Question 12

    1 mark

    The distance between (1, 2) and (4, 6) is ___

    A. 5

    B. 7

    C. 4

    D. 3

    (1 mark)

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