The change which is indistinguishable to rotating a number 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 whereby and also are real numbers.

If and are optimistic then the allude If we revolve the coordinate  counterclockwise then the coordinates end up being .

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

The coordinate If us reflect the name: coordinates around the -axis then the coordinates end up being .

The coordinate This means that rotating a figure counterclockwise is indistinguishable to change of reflecting over -axis and reflecting over -axis.

Option (A)

In option (A) it is provided that reflection around the line is tantamount to rotating a number counterclockwise.

If we reflect the coordinate  then the coordinates come to be .

This is not same as rotating the number counterclockwise.

Therefore, the option (A) is incorrect.

Option (B)

In option (B) the is offered that reflection about is equivalent to rotating a number counterclockwise.

If we reflect the coordinate  then the coordinates become .

This is not exact same as rotating the number counterclockwise.

Therefore, the option (B) is incorrect.

Option (C)

In option (C) the is given that reflection around -axis and also -axis is tantamount to rotating a number counterclockwise.

If us reflect the name: coordinates  -axis and -axis then the coordinates end up being .

This is exact same as rotating the figure counterclockwise.

Therefore, the option (C) is correct.

Option (D)

In option (D) it is given that shifting a allude devices left and also units down is indistinguishable to rotating a figure counterclockwise.

If we change the allude , systems left and also units down the name: coordinates 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 photo are in type (h,k).

The resulting works with of photo rotation of 180° around the beginning would be (-h,-k).

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

We deserve to see the x-coordinate is being multiplied through -1 and also then y-coordinate is also being multiply by -1.

Above rule could be break into two parts.

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

We have the right to see in an initial step, (h,k) ---> (-h,k) is being reflecting over the x-axis and