Mathematics
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.
Reflection
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Answer
The graph for the question is shown below:
(i) Since, point P lies on y-axis.
Hence, the point P(0, 5) is invariant in y-axis.
(ii) From graph we get,
The image of Q(-2, 4) on reflection in y-axis is Q'(2, 4).
(iii) Given, (0, k) on reflection in the origin is invariant.
A point is invariant on reflection in origin if it lies on it, i.e. point = (0, 0).
Comparing (0, 0) with (0, k) we get : k = 0.
Hence, the value of k = 0.
(iv) From graph we get,
On reflecting in origin,
Q ⇒ Q"
On reflecting in x-axis,
Q" ⇒ Q'
The coordinates of image of Q after reflection in origin and then in x-axis is (2, 4).
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Related Questions
Use a graph paper for this question (Take 2 cm = 1 unit on both x and y axis).
(i) Plot the following points : A(0, 4), B(2, 3), C(1, 1) and D(2, 0)
(ii) Reflect points B, C, D on the y-axis and write down their co-ordinates. Name the images as B', C', D' respectively.
(iii) Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation of the line of symmetry of the figure formed.
(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".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) originThe 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'.