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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.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
2.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
3.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
(a)48
(b)14
(c)24
(d)28
4.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
(a)1
(b)5
(c)0
(d)6
5.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)
6.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)
7.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
(a)18
(b)36
(c)13
(d)26
8.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
(a)3
(b)7
(c)14
(d)5
9.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
(a)22
(b)28
(c)35
(d)63
10.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
(a)(5, 2)
(b)(−5, −2)
(c)(−5, 2)
(d)(2, 5)
11.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
12.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
13.Work out the distance between the point (0, 0) and the point (5, 12).
(a)12
(b)13
(c)17
(d)7
14.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)
15.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)

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