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.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 2.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.
- 3.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
- 4.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.
- 5.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
- 6.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.
- 7.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
- 8.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
- 9.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
- 10.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
- 11.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
- 12.Work out the distance between the points (−3, 4) and (5, −2).
- 13.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.
- 14.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
- 15.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.
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