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