Reflection

14 Grade 10 Essential Mathematics questions on Reflection, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   3 marks

   State three properties of a figure that remain unchanged when the figure is reflected in a mirror line.

   (3 marks)

   Marking scheme

   Any three of the following, 1 mark each: (i) the lengths of all sides are unchanged, so object and image are congruent; (ii) the sizes of all angles are unchanged; (iii) the area of the figure is unchanged; (iv) lines that were parallel in the object remain parallel in the image. Maximum 3 marks.

2. Question 2

   4 marks

   A shopkeeper paints the word MAT in capital letters on the inside of a glass window. Seen from outside, the word reads TAM, yet each individual letter still looks correctly formed. Explain this observation.

   (4 marks)

   Marking scheme

   The glass acts as a vertical mirror line, so the writing is reflected left to right — 1 mark. Reflection reverses the sense (order) of the figure, so the letter that was first, M, now appears last — 1 mark, giving the order T, A, M — 1 mark. Each of the letters M, A and T has a vertical line of symmetry, so reflecting an individual letter in a vertical line maps it onto itself and it looks unchanged — 1 mark.

3. Question 3

   4 marks

   Under a reflection, the point D(3, 1) maps onto D'(3, 9). State the equation of the mirror line and explain how you obtained it.

   (4 marks)

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4. Question 4

   1 mark

   A point P is 4 cm from a mirror line, the distance being measured along the perpendicular from P to that line. Calculate the distance between P and its image P' under reflection in the line.

   A. 8 cm

   B. 16 cm

   C. 2 cm

   D. 4 cm

   (1 mark)

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5. Question 5

   2 marks

   The point A(6, -4) is reflected in the y-axis to give the image A'. State the coordinates of A' and state the distance of A from the mirror line.

   (2 marks)

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6. Question 6

   1 mark

   Under a reflection in the x-axis, the image of a point Q is Q'(-3, 8). Identify the coordinates of the object point Q.

   A. (-3, -8)

   B. (8, -3)

   C. (3, 8)

   D. (-3, 8)

   (1 mark)

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7. Question 7

   3 marks

   Describe how to locate, by construction, the image of a single point under a reflection in a given mirror line.

   (3 marks)

   Marking scheme

   Draw a line from the point perpendicular to the mirror line — 1 mark. Measure the distance from the point to the mirror line along that perpendicular — 1 mark. Mark the image on the opposite side of the mirror line, on the same perpendicular and at the same measured distance from the line — 1 mark.

8. Question 8

   1 mark

   The point T(7, 2) is reflected in the line x = 3. State the coordinates of the image of T.

   A. (1, 2)

   B. (7, 4)

   C. (-1, 2)

   D. (-7, 2)

   (1 mark)

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9. Question 9

   4 marks

   A triangle has vertices P(1, 2), Q(4, 2) and R(4, 6). The triangle is reflected in the x-axis. State the coordinates of P', Q' and R', and state the length of P'Q'.

   (4 marks)

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10. Question 10

    1 mark

    A paving slab at the entrance of a county office is cut in the shape of a regular hexagon. State the number of lines of symmetry the slab has.

    A. 3

    B. 2

    C. 12

    D. 6

    (1 mark)

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11. Question 11

    3 marks

    A tailor in Kisumu wants to cut two matching sleeve pieces for a shirt. Describe how the tailor can use reflection to obtain them from one piece of cloth.

    (3 marks)

    Marking scheme

    Fold the cloth once so that the fold line acts as the mirror line — 1 mark. Draw and cut out one sleeve shape through both layers of the folded cloth at the same time — 1 mark. Opening out the cloth gives two pieces that are congruent mirror images of each other, one suited to the left arm and one to the right — 1 mark.

12. Question 12

    1 mark

    A kanga design is reflected in a mirror line to produce an image. State which feature of the design is NOT the same in the image as in the object.

    A. The sizes of the angles in the design

    B. The sense (the left-to-right order) of the design

    C. The area covered by the design

    D. The lengths of the sides of the design

    (1 mark)

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13. Question 13

    1 mark

    A shape drawn on the Cartesian plane is reflected in the y-axis. Identify the point below that maps onto itself.

    A. (0, 7)

    B. (7, 7)

    C. (7, 0)

    D. (-7, 0)

    (1 mark)

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14. Question 14

    1 mark

    The point R(-5, 2) is reflected in the line y = x. State the coordinates of its image.

    A. (-5, -2)

    B. (5, -2)

    C. (-2, 5)

    D. (2, -5)

    (1 mark)

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