Mathematics
Use a graph paper for this question. Plot the points P(3, 2) and Q(-3, -2). From P and Q, draw perpendiculars PM and QN on the x-axis.
(i) Name the image of P on reflection in the origin.
(ii) Assign the special name to the geometrical figure PMQN and find its area.
(iii) Write the co-ordinates of the point to which M is mapped on reflection in
(a) x-axis
(b) y-axis
(c) origin
Reflection
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Answer
The graph for the question is shown below:
(i) From graph we get,
The coordinates of image of P after reflection in origin is Q(-3, -2).
(ii) From figure,
PMQN is a parallelogram.
Area of parallelogram = Base × Height
= QN × MN
= 2 × 6
= 12 sq.units.
Hence, PMQN is a // gm and area of PMQN = 12 sq. units
(iii) Since, M lies on x-axis it is invariant on reflection in x-axis. Thus, coordinates remain same (3, 0).
From graph,
On reflection in y-axis and origin the coordinates of M becomes (-3, 0).
Hence, coordinates of M on reflection in x-axis, y-axis and origin are (3, 0), (-3, 0), and (-3, 0) respectively.
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Related Questions
(i) Plot the points A(3, 2) and B(5, 4) on a graph paper.
(ii) Reflect A and B in the x-axis to A' and B' respectively. Plot A' and B' on the same graph paper. Write the co-ordinates of A' and B'.
(iii) Write down :
(a) the geometrical name of the figure ABB'A'.
(b) m∠ABB'.
(c) the image A" of A when reflected in the origin.
(d) the single transformation that maps A' to A".Points P and Q have co-ordinates (0, 5) and (-2, 4).
(i) P is invariant when reflected in an axis. Name the axis.
(ii) Find the image of Q on reflection in the axis found in (1).
(iii) (0, k) on reflection in the origin is invariant. Write the value of k.
(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in the x-axis.
The point P(3, 4) is reflected to P' in x-axis and O' is the image of O (origin) when reflected in the line PP'.
Using graph paper, give :
(i) the co-ordinates of P' and O'.
(ii) the length of the segments PP' and OO'.
(iii) the geometrical name of the figure POP'O'.
(iv) the perimeter of the quadrilateral POP'O'.
Use a graph paper for this question. A(1, 1), B(5, 1), C(4, 2) and D(2, 2) are the vertices of a quadrilateral.
(i) Name the quadrilateral ABCD.
(ii) A, B, C, D are reflected in the origin onto A', B', C' and D' respectively. Locate A', B', C', D' on the graph paper and write their co-ordinates.
(iii) Are D, A, A' and D' collinear?