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Standard X

Mathematics

Invariant Points

i Plot the po...

Question

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper.

(iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA'BB'.

(v) Name two invariant points under reflection in the x-axis.

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Solution

(i) The points A (3, 5) and B (-2, -4) can be plotted on a graph as shown.

(ii) A’ = Image of A when reflected in the x-axis = (3, -5)

(iii) C = Image of B when reflected in the y-axis = (2, -4)
B’ = Image when C is reflected in the origin = (-2, 4)

(iv) Isosceles trapezium

(v) Any point that remains unaltered under a given transformation is called an invariant.
Thus, the required two points are (3, 0) and (-2, 0).

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Similar questions

Q. Using graph paper and taking

1 c m = 1

unit along both

x

-axis and

y

-axis.
(i) Plot the points

A (- 4, 4)

and

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(ii) Reflect

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in the origin to get images

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(iii) Write down the co-ordinates of

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(iv) Give the geometrical name for the figure

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(v) Draw and name its lines of symmetry.

P and Q have co-ordinates (0, 5) and (-2, 4).

(a) P is invariant when reflected in an axis. Name the axis.

(b) Find the image of Q on reflection in the axis found in (a)

(d) Write the co-ordinates of the image of Q, obtained by reflection it in the origin followed by reflection in x-axis.

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2 c m = 1

unit on both axis), plot

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and

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Attempt this question on graph paper.

(a) Plot A (3, 2) and B (5, 4) on graph paper.

(b) Reflect A and B in the x-axis to A' and B' respectively. Plot these points also on the same graph paper.

(i) the geometrical name of the figure ABB' A';

(ii) the measure of angle ABB';

(iii) the image A" of A, when A is reflected in the origin.

(iv) the single transformation that maps A' to A".

(i) Point P (a, b) is reflected in the x-axis to P' (5, -2). Write down the values of a and b.

(ii) P" is the image of P when reflected in the y-axis. Write down the co-ordinates of P".

(iii) Name a single transformation that maps P' to P".

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