Coordinates & Graphs

13 Grade 8 Mathematics questions on Coordinates & Graphs, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   1 mark

   Find the gradient of the line joining the points (1, 2) and (4, 11).

   A. 9

   B. $\frac{1}{3}$

   C. 3

   D. $\frac{13}{5}$

   (1 mark)

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2. Question 2

   3 marks

   The points A(1, 2), B(5, 2) and C(5, 5) are three vertices of a rectangle. Find the coordinates of the fourth vertex D.

   (3 marks)

   Marking scheme

   In a rectangle the sides are parallel to the axes here: $A(1,2)$ and $B(5,2)$ share the same $y$, and $B(5,2)$ and $C(5,5)$ share the same $x$. (1)

   $D$ is opposite $B$, so it takes its $x$ from $A$ and its $y$ from $C$: $x=1$ and $y=5$. (1)

   That gives $D(1,5)$, and $AD$ is vertical while $DC$ is horizontal, as a rectangle needs. (1)

   Final answer: $D(1,5)$.

3. Question 3

   1 mark

   What are the coordinates of the origin?

   A. (1, 1)

   B. (0, 1)

   C. (0, 0)

   D. (1, 0)

   (1 mark)

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4. Question 4

   4 marks

   A straight line passes through the points (0, 1) and (2, 5).

   (a) Find the gradient of the line. (2 marks)

   (b) Write the equation of the line. (2 marks)

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5. Question 5

   1 mark

   A point has coordinates (5, -2). What is its x-coordinate?

   A. -2

   B. 3

   C. 7

   D. 5

   (1 mark)

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6. Question 6

   1 mark

   Find the midpoint of the line joining (2, 3) and (6, 7).

   A. (8, 10)

   B. (2, 2)

   C. (3, 4)

   D. (4, 5)

   (1 mark)

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7. Question 7

   1 mark

   For the line $y=2x+1$, what is the value of y when x = 3?

   A. 5

   B. 6

   C. 7

   D. 10

   (1 mark)

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8. Question 8

   3 marks

   A straight line has gradient 2 and passes through the point (0, -3).

   (a) State the y-intercept. (1 mark)

   (b) Write the equation of the line. (2 marks)

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9. Question 9

   1 mark

   In which quadrant does the point (-4, -1) lie?

   A. Third quadrant

   B. Second quadrant

   C. Fourth quadrant

   D. First quadrant

   (1 mark)

   Marking scheme

   A. Third quadrant — 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.

10. Question 10

    1 mark

    On which axis does the point (0, -5) lie?

    A. y-axis

    B. x-axis

    C. Neither axis

    D. Both axes

    (1 mark)

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11. Question 11

    1 mark

    In which quadrant does the point (6, -3) lie?

    A. First quadrant

    B. Second quadrant

    C. Third quadrant

    D. Fourth quadrant

    (1 mark)

    Marking scheme

    D. Fourth quadrant — $x$ is positive and $y$ 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

    In which quadrant does the point (-3, 4) lie?

    A. First quadrant

    B. Second quadrant

    C. Third quadrant

    D. Fourth quadrant

    (1 mark)

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13. Question 13

    1 mark

    On which axis does the point (3, 0) lie?

    A. y-axis

    B. x-axis

    C. Origin

    D. Both axes

    (1 mark)

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