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Geometrical problems on coordinate axes worksheet — GCSE Foundation

Fifteen questions on "geometrical problems on coordinate axes" — DfE statement G11. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Geometrical problems on coordinate axes worksheet — GCSE Foundation

Maths · GCSE Foundation · G11 · Geometrical problems on coordinate axes · Non-calculator · 15 questions

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1.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?
(a)(0, 0) and (1, 1)
(b)(1, 2) and (2, 1)
(c)(2, 4) and (6, 4)
(d)(3, 5) and (3, 8)
2.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
3.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.
(a)(−1, 1)
(b)(5, 9)
(c)(5, 1)
(d)(2, 1)
4.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
(a)the origin
(b)y-axis
(c)both axes
(d)x-axis
5.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
(a)(5, 7)
(b)(2, 2)
(c)(4, 8)
(d)(6, 10)
6.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.
(a)18 units
(b)7 units
(c)14 units
(d)12 units
7.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
8.Work out the distance between the point (0, 0) and the point (5, 12).
(a)12
(b)13
(c)17
(d)7
9.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.
(a)Horizontal, because both points have a y-coordinate
(b)Neither, because both coordinates differ
(c)Horizontal, because the x-coordinates increase from A to B
(d)Vertical, because both points have an x-coordinate
10.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
(a)(−2, 6)
(b)(−2, −2)
(c)(7, −3)
(d)(8, 6)
11.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.
(a)Q, since OQ = 5 and OP = 6
(b)P, since OP = 5 and OQ = 6
(c)P, since OP = 6 and OQ = 5
(d)They are equally distant from the origin
12.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
(a)(3, −4)
(b)(−4, 3)
(c)(4, 3)
(d)(−4, −3)
13.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.
(a)No, since AB, BC and CA are not all equal
(b)Yes, since 4² + 5² = 3²
(c)No, since 3 + 4 ≠ 5
(d)Yes, since 3² + 4² = 5²
14.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
(a)zero
(b)negative
(c)cannot be determined
(d)positive
15.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.
(a)Parallel, since both gradients are 2
(b)Not parallel, since the gradients are 2 and 4
(c)Parallel, since both lines pass through positive coordinates
(d)Not parallel, since the two lines cross the y-axis at different points

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