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