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.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.
- 2.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
- 3.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?
- 4.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 5.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 6.Work out the distance between the points (−3, 4) and (5, −2).
- 7.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
- 8.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
- 9.Work out the distance between the point (0, 0) and the point (5, 12).
- 10.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
- 11.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.
- 12.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.
- 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.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
- 15.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
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