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
Points (8, 0) and (-3, 0) are invariant points under reflection in the line L1, points (0, -9) and (0, 5) are invariant points under reflection in the line L2.
(i) Name or write down equations of the lines L1 and L2.
(ii) Write down the images of points P(3, 5) and Q(-8, 3) after reflection in line L1. Name the images as P' and Q' respectively.
(iii) Write down the images of P and Q on reflection in L2. Name the images as P" and Q" respectively.
(iv) Describe a single transformation that maps P' to P".
ABC is a triangle as shown in the figure below.
(a) Write down the coordinates of A, B and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.
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.
(a) Point P(2, -3) on reflection becomes P'(2, 3). Name the line of reflection (say L1).
(b) Point P' is reflected to P'' along the line (𝐿2), which is perpendicular to the line 𝐿1 and passes through the point, which is invariant along both axes. Write the coordinates of P''.
(c) Name and write the coordinates of the point of intersection of the lines 𝐿1 and 𝐿2.
(d) Point P is reflected to P''' on reflection through the point named in the answer of part I of this question. Write the coordinates of P'''. Comment on the location of the points P'' and P'''.