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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

Maths · GCSE Foundation · G11 · Geometrical problems on coordinate axes · 15 questions

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1.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.
(a)(3, −4)
(b)(−4, 3)
(c)(4, 3)
(d)(−4, −3)
2.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.
(a)No, since AB, BC and CA are not all equal
(b)Yes, since 4² + 5² = 3²
(c)No, since 3 + 4 ≠ 5
(d)Yes, since 3² + 4² = 5²
3.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
(a)third quadrant
(b)second quadrant
(c)first quadrant
(d)fourth quadrant
4.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.
(a)26.00 units
(b)4.47 units
(c)10.00 units
(d)7.21 units
5.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
(a)(−2, 6)
(b)(−2, −2)
(c)(7, −3)
(d)(8, 6)
6.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
(a)3
(b)7
(c)14
(d)5
7.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
(a)22
(b)28
(c)35
(d)63
8.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
(a)(5, 7)
(b)(2, 2)
(c)(4, 8)
(d)(6, 10)
9.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
10.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.
(a)(−1, 1)
(b)(5, 9)
(c)(5, 1)
(d)(2, 1)
11.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.
(a)Q, since OQ = 5 and OP = 6
(b)P, since OP = 5 and OQ = 6
(c)P, since OP = 6 and OQ = 5
(d)They are equally distant from the origin
12.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
13.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.
(a)Parallel, since both gradients are 2
(b)Not parallel, since the gradients are 2 and 4
(c)Parallel, since both lines pass through positive coordinates
(d)Not parallel, since the two lines cross the y-axis at different points
14.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
(a)the origin
(b)y-axis
(c)both axes
(d)x-axis
15.A vertical line passes through the point (5, 2). Write down the equation of this line.
(a)x = 2
(b)x = 5
(c)y = 2
(d)y = 5

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