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
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.
Study the graph and answer each of the following :
(a) Write the coordinates of points A, B, C and D.
(b) Given that, point C is the image of point A. Name and write the equation of the line of reflection.
(c) Write the coordinates of the image of the point D under reflection in y-axis.
(d) What is the name given to a point whose image is the point itself ?
(e) On joining the points A, B, C, D and A in order, a figure is formed. Name the closed figure.
Use graph sheet for this question.
(a) Plot A(0, 3), B(2, 1) and C(4, -1).
(b) Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.
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(d) Plot and write coordinates of point A'.
(e) Join the points ABA'B' and give the geometrical name of the closed figure so formed.
Plot the points A(2, 2) and B(6, -2) in the graph and answer the following :
(a) Reflect points A in origin to point D and write the co-ordinates of point D.
(b) Reflect points A in line y = -2 to point C and write the co-ordinates of point C.
(c) Find a point P on CD which is invariant under reflection in x = 0, write its co-ordinates.
(d) Write the geometrical name of the closed figure ABCD.
(e) Write the co-ordinates of the point of intersection of the diagonals of ABCD.