Mathematics
Study the graph and answer each of the following:
(i) Write down the co-ordinates of A, B and C. Reflect point A in x-axis and mark as A'.
(ii) Name the invariant point in 2nd quadrant on reflection in x-axis.
(iii) Join the points ABA'C. Name the figure formed.
Reflection
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Answer
(i) A = (0, 4), B = (-4, 0) and C = (4, 0)
(ii) B
(iii) Square
Reason
From graph,
Co-ordinates of A = (0, 4), B = (-4, 0) and C = (4, 0).
Since, point B is in 2nd quadrant and it lies on x-axis and on reflection in x-axis it remains there only. Thus, B is invariant.
By formula,
Slope =
Slope of AB = = 1
Slope of A'B = = -1.
Since, product of slope of AB and A'B is -1.
Thus, AB and A'B are perpendicular to each other. Since, all sides are equal and angle between sides = 90°.
∴ ABA'C is a square.
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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".
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’.
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.
