A point A is reflected in the origin $(M_{0})$ and then in y-axis $(M_{y})$ after which the new point is A'. Which single transformation maps A onto A' ?

$M_{y} . M_{x}$

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$M_{x} . M_{0}$

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$M_{x}$

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None of the above

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Solution

The correct option is C
$M_{x}$

Let point A be (x, y)

Image of A(x , y) when reflected in the origin is (-x, -y)

Image of A(-x , -y) when reflected in the y axis (x, -y)

The operation $M_{x}$ on A(x, y) will result in (x, -y) which is same as $M_{0}, M_{y}$ .

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Similar questions

The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A".

(i) Write down the co-ordinates of A".

(ii) Write down a single transformation that maps A onto A".

The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A".

(i) Write down the co-ordinates of A".

(ii) Write down a single transformation that maps A onto A".

The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C".

(i) Write down the co-ordinates of A", B" and C".

(ii) Write down a single transformation that maps triangle ABC onto triangle A" B" C".

(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".

Find the image of point (4, -6) under the following operations :

(i) $M_{x} . M_{y}$ (ii) $M_{y} . M_{x}$

(iii) $M_{o} . M_{x}$ (iv) $M_{x} . M_{o}$

(v) $M_{o} . M_{y}$ (vi) $M_{y} . M_{o}$

Write down a single transformation equivalent to each operation given above.

State whether :

(a) $M_{o} . M_{x}$ = $M_{x} . M_{o}$

(b) $M_{y} . M_{o}$ = $M_{o} . M_{y}$

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A point A is reflected in the origin (M0) and then in y-axis (My) after which the new point is A'. Which single transformation maps A onto A' ?

The correct option is C Mx Let point A be (x, y) Image of A(x , y) when reflected in the origin is (-x, -y) Image of A(-x , -y) when reflected in the y axis (x, -y) The operation Mx on A(x, y) will result in (x, -y) which is same as M0,My.

A point A is reflected in the origin $(M_{0})$ and then in y-axis $(M_{y})$ after which the new point is A'. Which single transformation maps A onto A' ?

The correct option is C
$M_{x}$

Let point A be (x, y)

Image of A(x , y) when reflected in the origin is (-x, -y)

Image of A(-x , -y) when reflected in the y axis (x, -y)

The operation $M_{x}$ on A(x, y) will result in (x, -y) which is same as $M_{0}, M_{y}$ .