# Form 2 Mathematics Questions and Answers on Reflection and Congruence

Form 2 Mathematics Questions and Answers on Reflection and Congruence

Lessons (**27**) * SHARE*

- 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.

7m 49s - 2.
The angle between an image line and its object line is 80°. Draw a diagram to show the position of the mirror line.

4m 21s - 3.
The figure below shows an object and its image after reflection. Trace them and draw the mirror line.

3m 5s - 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.

24m 23s - 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

11m 44s - 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.

13m 18s - 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.

34m 43s - 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.

6m 9s - 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.

2m 43s - 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.

4m 55s - 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.

6m 55s - 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.

9m 17s - 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)

4m 27s - 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)

10m 24s - 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.

6m 29s - 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.

18m 59s - 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.

8m 37s - 18.
Plot points A(4, 1) and B(2, 5).
(a) Calculate the distance AB.
(b) Reflect line AB along the line y = -x.

7m 23s - 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.

9m 58s - 20.
Given point L(2, 1) and L'(6, 1), the image of L under a reflection, find the equation of the mirror line.

2m 56s - 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.

6m 0s - 22.
In the figure PQ = PS and QR = RS. Show that #triangle# PQR and #triangle# PSR are congruent.

1m 24s - 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.

1m 26s - 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.

2m 0s - 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.

4m 21s - 26.
In the figure below, PS = QR = PX = XQ. Show that #triangle# PQS and #triangle# PQR are congruent.

1m 33s - 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.

5m 8s

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