Printable · GCSE Foundation · ages 14-16
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
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- 1.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
- 2.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.
- 3.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 4.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.
- 5.Work out the distance between the point (0, 0) and the point (5, 12).
- 6.Work out the distance between the points (−3, 4) and (5, −2).
- 7.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 8.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.
- 9.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
- 10.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
- 11.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
- 12.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?
- 13.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.
- 14.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
- 15.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
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