The transformation which is equivalent to rotating a figure counterclockwise is reflecting over the -axis and -axis. Therefore, the is correct.

You are watching: Which transformation will be equivalent to rotating a figure 180° counterclockwise?

Further explanation:

Consider a coordinate in the form where and are real numbers.

If and are positive then the point If we rotate the coordinate  counterclockwise then the coordinates become .

The coordinate If we reflect the coordinate  -axis then the coordinates become .

The coordinate If we reflect the coordinate  -axis then the coordinates become .

The coordinate This implies that rotating a figure counterclockwise is equivalent to transformation of reflecting over -axis and reflecting over -axis.

Option (A)

In option (A) it is given that reflection about the line is equivalent to rotating a figure counterclockwise.

If we reflect the coordinate  then the coordinates become .

This is not same as rotating the figure counterclockwise.

Therefore, the option (A) is incorrect.

Option (B)

In option (B) it is given that reflection about is equivalent to rotating a figure counterclockwise.

If we reflect the coordinate  then the coordinates become .

This is not same as rotating the figure counterclockwise.

Therefore, the option (B) is incorrect.

Option (C)

In option (C) it is given that reflection about -axis and -axis is equivalent to rotating a figure counterclockwise.

If we reflect the coordinate  -axis and -axis then the coordinates become .

This is same as rotating the figure counterclockwise.

Therefore, the option (C) is correct.

Option (D)

In option (D) it is given that shifting a point units left and units down is equivalent to rotating a figure counterclockwise.

If we shift the point , units left and units down the coordinate is .

This is not same as rotating the figure counterclockwise.

Therefore, the option (D) is incorrect.

Therefore, the is correct.

historicsweetsballroom.com details:

Subject: Mathematics

Chapter: Geometry

Keywords: Transformation, rotation, reflection, clockwise, geometry, counterclockwise, -axis, - axis, coordinates, graph, origin, line, degrees, translation, symmetry. If we have given coordinates of the image are in form (h,k).

The resulting coordinates of image rotation of 180° around the origin would be (-h,-k).

We have rule (h,k) ---> (-h,-k).

We can see that x-coordinate is being multiplied by -1 and then y-coordinate is also being multiplied by -1.

Above rule could be break into two parts.

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### (h,k) ---> (-h,k) ----> (-h,-k).

We can see in first step, (h,k) ---> (-h,k) is being reflecting over the x-axis and