Mathematics
Study the graph and answer the following questions :
(i) Write down the co-ordinates of A, B and C.
(ii) Reflect A, B and C in origin and mark the points as F, E and D respectively. Write down the co-ordinates of D, E and F.
(iii) Is BC and DE parallel ? Justify your answer.
Reflection
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Answer
A = (-3, 1), B = (0, 3), C = (-2, -2); D = (2, 2), E = (0, -3), F = (3, -1); yes, as slope of BC and DE are equal.
Reason
From graph,
Co-ordinates of A = (-3, 1), B = (0, 3), C = (-2, -2), D = (2, 2), E = (0, -3), F = (3, -1)
By formula,
Slope =
Slope of BC =
Slope of DE =
We know that,
Slope of parallel lines are equal.
Slope of BC = Slope of DE.
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Related Questions
Plot points A(0, 3), B(4, 0), C(6, 2) and D(5, 0). Reflect the points as given below and write their coordinates :
(a) Reflect A on x-axis to A’.
(b) Reflect B on y-axis to B’.
(c) Reflect C on x-axis to C’.
(d) D remain invariant when reflected on the line whose equation is …………… .
(e) Join the points A, B, C, D, C’, B, A’, B’ and A to form a closed figure. Name the closed figure BCDC’.
Use graph sheet for this question. Take 2 cm = 1 unit along the axes.
(a) Plot A(1, 2), B(1, 1) and C(2, 1)
(b) Reflect A, B and C about y-axis and name them as A', B' and C'.
(c) Reflect A, B, C, A', B' and C' about x-axis and name them as A'', B'', C'', A''', B''' and C''' respectively.
(d) Join A, B, C, C'', B'', A'', A''', B''', C''', C', B' , A' and A to make it a closed figure.
Use graph paper for this question :
Use 1 cm = 1 unit on both the axes.
(i) Plot the points A(4, 5) and B(-1, -3)
(ii) A' is the image of A when reflected in the y-axis. Write down the co-ordinates of A' and plot it on the graph paper.
(iii) B' is the image of B when reflected in the x-axis followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.
(iv) Write down the geometrical name of the figure AA'BB'.
(v) Name two invariant points under reflection in y-axis.
Use graph sheet to answer this question. Take 2 cm = 1 unit along both the axes.
(a) Plot A, B, C where A(0, 4), B(1, 1) and C(4, 0).
(b) Reflect A and B on the x-axis and name them as E and D respectively.
(c) Reflect B through the origin and name it F. Write down the coordinates of F.
(d) Reflect B and C on the y-axis and name them as H and G respectively.
(e) Join points A, B, C, D, E, F, G, H and A in order and name the closed figure formed.