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Form 2 Mathematics Questions and Answers on Reflection and Congruence

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