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Form 2 Similarity and Enlargement Topical Questions and Answers

Form 2 Similarity and Enlargement Topical Questions and Answers

Lessons (25)

• 1.    Points A (4, 2), B (9, 2), C(7, -2) and D (2, -2) are the vertices of a parallelogram. Taking the origin as the centre of enlargement, find the image when the scale factor is -1
  9m 3s

• 2.    Points A (4, 2), B (9, 2), C(7, -2) and D (2, -2) are the vertices of a parallelogram. Taking the origin as the centre of enlargement, find the image when the scale factor is - #1/4#.
  10m 29s

• 3.    State the centre of enlargement and the linear scale factor in each of the following figures if #triangle# A'B'C' is the image of #triangle# ABC:
  3m 26s

• 4.    In #triangle# ABC, AB = 3 cm, BC = 4 cm and AC = 5 cm. The sides AB, BC and AC are enlarged by a linear scale factor of 2.5. Find the length of the new triangle.
  2m 34s

• 5.    If a road 8 km long is represented by 4 cm on a map, find the scale of the map.
  1m 28s

• 6.    A rectangle measures 3 cm by 5 cm. Find the corresponding measurements of the image of the rectangle after an enlargement of scale factor: (a) - 0.75 (b) -1.5 (c) -3
  1m 53s

• 7.    The radius of a circle is 3.5 cm. Find the circumference of its image after an enlargement of scale factor 1.75.
  1m 24s

• 8.    A triangular field PQR is such that PQ = 20 m, PR = 30 m and QR = 40 m. The field is drawn to scale such that the side PQ is 3 cm long. Find the linear scale factor and the lengths of QR and PR.
  3m 1s

• 9.    The figure below shows a cone of base radius 28 cm and the slant side of length 35 cm. At a point P, 14 cm vertically below the vertex, the cone is cut across to form a smaller one. Calculate the base radius of the smaller cone.
  3m 4s

• 10.    A floor in a plan of a house measures 20 cm by 13 cm. Find the area of the actual house if the linear scale factor is 50.
  1m 53s

• 11.    The corresponding lengths of two similar photographs are 12 cm and 30 cm. The area of the larger photograph is 750 #cm^2#. Find the: (a) area scale factor. (b) area of the smaller photograph.
  1m 44s

• 12.    The floor of a room measuring 15 m by 9 m requires 3 375 square tiles. Find the measurements of each tile. If the tiles available were twice as long, determine the number of tiles that would be required.
  3m 38s

• 13.    The ratio of the area of two similar rooms is #4/25# (a) Find the area of the bigger room if the area of the smaller room is 8#m^2#. (b) Find the ratio of their lengths. (c) If the length of the larger room is 10 m, find the length of the smaller one.
  1m 44s

• 14.    The corresponding sides of two similar regular pentagons are 3 cm and 7 cm respectively. (a) Find the ratio of their areas. (b) Calculate the area of the larger if the area of the smaller is 36 #cm^2#.
  1m 28s

• 15.    Mwangi has two balloons, one yellow and the other green. The radius of the yellow balloon is 7 cm while that of the green balloon is 21 cm. Find the ratio of their surface areas.
  1m 6s

• 16.    (a) In the figure below, name three pairs of (i) Corresponding sides. (ii) Corresponding angles. (b) What can you say about triangles AOB and COD?
  2m 22s

• 17.    In the figure below, triangle ABE is similar to triangle ACD. Calculate the length of BC.
  1m 47s

• 18.    In the figure below, SR is parallel to PQ. Calculate the lengths of SR and PX.
  2m 53s

• 19.    In the figure below, #angle# EHG = #angle# EFH = 90°, HF = 5 cm and EF = 12 cm. Calculate the length HG and FG.
  4m 35s

• 20.    A triangle KLM is similar to a triangle PQR. KL = 5 cm, LM = 4 cm and #angle# KLM = 46°. Construct triangle PQR such that QR = 6 cm.
  6m 22s

• 21.    ABCD and PQRS are similar rectangles. AB = 3 cm and BC = 7 cm. If PQ = 5 cm, construct rectangle PQRS.
  6m 9s

• 22.    WXYZ is a rectangle in which WX = 8 cm and XY = 6 cm. F is a point on YZ such that YF = 6 cm. Construct a rectangle YEFG similar to WXYZ such that YF is the diagonal.
  7m 24s

• 23.    In the figure below, #angle# TQS = #angle# QPR, PR//TS, PQ = 15 cm, QR = 6 cm and ST = 8 cm. Calculate QT.
  2m 31s

• 24.    The vertices of an object and its image after an enlargement are A(0, 0), B (1, 1), C (2, 0), D(1, -1) and A'(3, 3), B'(5, 5), C'(7, 3), D'(5, 1) respectively. Find the centre and scale factor of the enlargement.
  8m 48s

• 25.    Given that P (3, 4), Q(4, 4), R(6, 4), S (7, 1) and T (5, 0) are the vertices of an object, find the vertices of the image after an enlargement with the centre at (0, 0) and scale factor #1/2#
  8m 38s