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 triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.
- 2.Work out the distance between the points (−3, 4) and (5, −2).
- 3.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.
- 4.A vertical line passes through the point (5, 2). Write down the equation of this line.
- 5.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?
- 6.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 7.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.
- 8.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 9.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.
- 10.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
- 11.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.
- 12.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.
- 13.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
- 14.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.
- 15.Work out the distance between the point (0, 0) and the point (5, 12).
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