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Geometrical problems on coordinate axes worksheet — GCSE Higher

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 Higher

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

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1.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
2.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
3.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
4.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
(a)18
(b)36
(c)13
(d)26
5.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.
(a)(6, 1)
(b)(1, 6)
(c)(1, 5)
(d)(9, 6)
6.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.
(a)120 units²
(b)60 units²
(c)30 units²
(d)65 units²
7.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.
(a)Horizontal, because both points have a y-coordinate
(b)Neither, because both coordinates differ
(c)Horizontal, because the x-coordinates increase from A to B
(d)Vertical, because both points have an x-coordinate
8.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).
(a)1
(b)5
(c)0
(d)6
9.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
10.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.
(a)9
(b)5
(c)20
(d)4
11.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
(a)(3, 3)
(b)(4, 0)
(c)(4, 3)
(d)(3.5, 3)
12.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)
13.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.
(a)48
(b)14
(c)24
(d)28
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.
(a)18 units
(b)7 units
(c)14 units
(d)12 units
15.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

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