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.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Geometrical problems on coordinate axes worksheet — GCSE Foundation

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

MathsUKwww.geekhero.co.uk

1.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
2.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
3.Work out the distance between the point (0, 0) and the point (5, 12).
(a)12
(b)13
(c)17
(d)7
4.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
5.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
6.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
(a)zero
(b)negative
(c)cannot be determined
(d)positive
7.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.
(a)Parallel, since A and D have the same x-coordinate
(b)Parallel, since AB and DC are both horizontal lines
(c)Not parallel, since AB is horizontal and DC is vertical
(d)Not parallel, since AB and DC have different lengths
8.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.
(a)0.2 hours
(b)25 hours
(c)5 hours
(d)125 hours
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.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)
11.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
12.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
13.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
14.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
15.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

Build your own mix at the worksheet builder.