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Form 2 Mathematics Questions and Answers on Reflection and Congruence
In the figure PQ = PS and QR = RS. Show that #triangle# PQR and #triangle# PSR are congruent.
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1.
An object line AB, 4 cm long, makes an angle of 35° with the mirror line at point B. Draw the image line and find the angle between A'B' and the mirror line.
2.
The angle between an image line and its object line is 80°. Draw a diagram to show the position of the mirror line.
3.
The figure below shows an object and its image after reflection. Trace them and draw the mirror line.
4.
The vertices of a quadrilateral ABCD are A(4.5, 1.5), B(7.5, 3), C(5, 3.5) and D(4.5, 2.5). Draw on the same axes the quadrilateral and its image after a reflection in the: (a) x-axis (b) line y = x. (c) y-axis (d) line y = -x.
5.
If A(2, -7), B(2, -2) and C(7, -2) are vertices of a triangle, find the image of the triangle under a reflection in the line: (a) y = -2.5 (b) x = 3.5
6.
A(-5, -2), B(-2, -5) and C(-12, -2) are vertices of a triangle. Find the image of the triangle when it is reflected in the: (a) y-axis followed by a reflection in the line y = -x. (b) x-axis followed by a reflection in the line y = x.
7.
The vertices of a polygon ABCDEF are A(- 4, 6), B(-3, 2), C(-7, 1), D(-7, 4), E(-8, 5) and F(-7, 6). Find the final image of the polygon under the reflection in the line: (a) y = x, followed by a reflection in y = -x. (b) y = x, followed by a reflection in y axis, and finally followed by one in the line y = -x.
8.
A circle with centre A(7, 4) and radius 3 units is reflected in the line x= 4.5, followed by a reflection in the y-axis. Draw the final image.
9.
A letter T has vertices (3, 8). (4, 8), (4, 6) and (5, 8). It is reflected in the x-axis. Draw the image of T.
10.
A letter N has vertices at(2, 6), (3, 6), (3, 8) and (4, 8). It is reflected in the y-axis followed by a reflection in the line y = 2. Determine the co-ordinates of the final image.
11.
The co-ordinates of the vertices of the letter V are (8, 4), (9, 2), and (10, 4). If the letter is reflected in the line x = - 2 followed by reflection in the line y=x, determine the co-ordinates of the: (a) first image. (b) final image.
12.
Line y= 2 intersects line x = 0. Find the equations of two possible mirror lines under which the lines will be images of each other.
13.
Find the equation of the bisector of the line joining each of the following pairs of points: (a) A(2, 8) and B(2, 10) (b) C(2, 8) and D(-2, 8)
14.
Find the equation of the bisector of the line joining each of the following pairs of points: (a) E(-2, -3) and F(- 4, -3) (b) G(2, - 4) and H(3, - 4) (c) I(5, 0) and J(0, 5)
15.
Draw triangle ABC, A(-2, -3), B(-4, - 4), and C(- 4, -2). (a) Name the type of triangle formed. (b) Write the equation of the mirror line if B and C are images of each other.
16.
Four of the vertices of an irregular octagon, which is symmetrical about line y = x, are A(1, -#1/2#), B(4, -3), C(4, 0) and D(3, 0). Find the co-ordinates of the remaining vertices. The octagon is reflected in the line y = 0. Find the equation of line of symmetry of the image.
17.
Plot points A(0, 5), B(3, 9), C(3, 4) and D(0, 0). (a) Name the quadrilateral ABCD. (b) Write down the equations of the two lines of symmetry.
18.
Plot points A(4, 1) and B(2, 5). (a) Calculate the distance AB. (b) Reflect line AB along the line y = -x.
19.
Plot points P(-3, 7), Q(-5, 3), R(-3, 1) and S(-1, 3). (a) Name the quadrilateral PQRS. (b) Find the equation of the line of symmetry. (c) Reflect figure PQRS in the line y = x and find the co-ordinates of its image. (d) Find the equation of the line of symmetry of the image.
20.
Given point L(2, 1) and L'(6, 1), the image of L under a reflection, find the equation of the mirror line.
21.
Draw triangle UVX with vertices U(1, 4), V(5, 4) and X(3, 1). UX and VX intersect at X. A point T is such that TX is the angle bisector of #angle#UXV. Locate one possible point of T and find the equation of TX.
22.
In the figure PQ = PS and QR = RS. Show that #triangle# PQR and #triangle# PSR are congruent.
23.
In the figure below, points A, B and C are on the circumference of the circle with centre O. Show that #triangle# AOB and #triangle# AOC are congruent.
24.
In the figure below, ABCD is a parallelogram. Line BE is parallel to line FD. Show that #triangle# ABE and #triangle# CDF are congruent.
25.
Two chords AB and AC of a circle are equal in length and the bisector of angle BAC meets the arc BC at D. Show that: (a) BD = DC (b) AD is perpendicular to BC.
26.
In the figure below, PS = QR = PX = XQ. Show that #triangle# PQS and #triangle# PQR are congruent.
27.
In a triangle ABC, AB = AC. H and K are points on AB and AC respectively, such that HK is parallel to BC. Show that #triangle# ABK and #triangle# ACH are congruent.
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