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