Geometry and measures worksheet — GCSE Foundation

1.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

2.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

3.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

4.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?

5.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

6.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

7.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

8.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

9.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

10.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

11.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

12.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

13.A polygon has 12 straight sides. What is the mathematical name for this polygon?

14.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

15.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.