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
*
lies in the first quadrant.

If we rotate the coordinate

*
*
counterclockwise then the coordinates become
*
.

The coordinate

*
lies in the third quadrant.

If we reflect the coordinate

*
about the
*
-axis then the coordinates become
*
.

The coordinate

*
lies in the fourth quadrant.

If we reflect the coordinate

*
about the
*
-axis then the coordinates become
*
.

The coordinate

*
lies in the third quadrant.

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

*
about the line
*
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

*
about the line
*
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

*
about
*
-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.

Learn more

1. Learn more about the rotation of the triangle about the origin brainly.com/question/7437053.

2. Learn more about when a triangle is rotated about the origin brainly.com/question/2992432.

historicsweetsballroom.com details:

Grade: High school

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