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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 · 15 questions

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1.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
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.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
4.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)
5.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
(a)third quadrant
(b)second quadrant
(c)first quadrant
(d)fourth quadrant
6.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)
7.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
8.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.
(a)(6, 1)
(b)(1, 6)
(c)(1, 5)
(d)(9, 6)
9.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
(a)(3, 3)
(b)(4, 0)
(c)(4, 3)
(d)(3.5, 3)
10.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.
(a)26.00 units
(b)4.47 units
(c)10.00 units
(d)7.21 units
11.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
12.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)
13.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)
14.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.
(a)9
(b)5
(c)20
(d)4
15.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

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