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Form 2 Similarity and Enlargement Topical Questions and Answers
In the figure below, SR is parallel to PQ. Calculate the lengths of SR and PX.
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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
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#.
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:
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.
5.
If a road 8 km long is represented by 4 cm on a map, find the scale of the map.
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
7.
The radius of a circle is 3.5 cm. Find the circumference of its image after an enlargement of scale factor 1.75.
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.
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.
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.
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.
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.
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.
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#.
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.
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?
17.
In the figure below, triangle ABE is similar to triangle ACD. Calculate the length of BC.
18.
In the figure below, SR is parallel to PQ. Calculate the lengths of SR and PX.
19.
In the figure below, #angle# EHG = #angle# EFH = 90°, HF = 5 cm and EF = 12 cm. Calculate the length HG and FG.
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.
21.
ABCD and PQRS are similar rectangles. AB = 3 cm and BC = 7 cm. If PQ = 5 cm, construct rectangle PQRS.
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.
23.
In the figure below, #angle# TQS = #angle# QPR, PR//TS, PQ = 15 cm, QR = 6 cm and ST = 8 cm. Calculate QT.
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.
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#
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