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Invariant Points

Points A-8,0,...

Question

Points A (-8,0), B (-16,0) are invariant points when reflected in the line $L_{1}$ . Find the image of the points C (-15,6) and D(8, 19) in the line $L_{1}$ .

A

(-15, -6), (8, 19)

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B

(-15, -6) ,(-8, 19)

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C

(15, 6) ,(-8, 19)

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D

(-15, -6) ,(-8, -19)

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Solution

The correct option is A
(-15, -6), (8, 19)

Any point that remains unaltered under a given transformation is called invariant.

Since points (-8,0), (-16,0) lie on X- axis, the points (-8,0) and (-16,0) are invariant when reflected in X - axis.

Hence, line $L_{1}$ is X- axis.

When any point is reflected in the X-axis the sign of y co-ordinate changes.

Hence, Image of point C (-15, 6) is (-15, -6) and image of point D (8, -19) is (8, 19)

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