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.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 2.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
- 3.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.
- 4.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.
- 5.Work out the distance between the points (−3, 4) and (5, −2).
- 6.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.
- 7.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
- 8.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
- 9.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 10.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 11.Work out the distance between the point (0, 0) and the point (5, 12).
- 12.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.
- 13.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
- 14.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
- 15.A vertical line passes through the point (5, 2). Write down the equation of this line.
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