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.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 2.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 3.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.
- 4.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.
- 5.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.
- 6.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 7.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
- 8.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?
- 9.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.
- 10.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.
- 11.Work out the distance between the point (0, 0) and the point (5, 12).
- 12.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
- 13.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.
- 14.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
- 15.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
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