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Form 2 Mathematics Questions and Answers on Reflection and Congruence

Lessons (27)

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

Form 2 Mathematics Questions and Answers on Reflection and Congruence

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