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