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.
Geometrical problems on coordinate axes worksheet — GCSE Foundation
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- 1.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
- 2.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 3.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
- 4.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
- 5.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.
- 6.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.
- 7.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
- 8.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 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.
- 10.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 11.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.
- 12.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
- 13.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
- 14.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.
- 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.
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