1. Defined as bounded through two distinctive end points the contain every point on the line in between its finish points.

You are watching: Which transformation will be equivalent to rotating a figure 90° counterclockwise?

B) line segment


A line segment is displayed by finish points ~ above each finish of the heat segment and is stood for by a line through arrows at each end.

2. If you revolve a right triangle, what feature of the triangle changes?

D) position of the triangle

When us rotate any figure, the angles and also sides continue to be the very same measure. The just thing that alters is that position.

3. Which revolution will be tantamount to rotating a figure 180° counterclockwise?


C) showing over the x-axis and also the y-axis.

When we rotate a number counterclockwise 180° , the coordinates readjust from (x, y) to (-x, -y).

Moving forward, once that number is reflected over the x axis the coordinates change from (x, y) come (x, -y).

Again showing it over the y-axis the coordinates change from (x, -y) to (-x,-y).

Therefore, we have the right to say that showing over the x-axis and also the y-axis will be equivalent to one 180° counterclockwise rotation.


C)Reflecting end the x-axis and then mirroring over the line y = x.

Step-by-step explanation:

A rotation 90° counterclockwise will certainly map every point (x, y) to (-y, x).

Since the x- and also y-coordinates are switched, this is not a reflection across the x-axis complied with by a reflection throughout the y-axis.

Since the y-coordinate is negated and the x- and y-coordinates space switched, this is not a translation.

Reflecting across the x-axis will negate the y-coordinate, giving us (x, -y). Complying with this v a reflection throughout y=x will switch the coordinates giving us (-y, x). This is the correct transformation.


D) showing over the y-axis and also then showing over the heat y = -x

Step-by-step explanation:

When the figure is rotate clock-wise or anti clock-wise then the coordinate of number is get adjusted and this new coordinate have the right to be discover on the communication of degree of rotation.

The rules of rotation is:

When rotation = 90° clock-wise, the vertices is get adjusted to (-y, x) native (x, y).When rotation = 180° clock-wise, the vertices is get changed to (-x, -y) from (x, y).When rotation = 270° clock-wise, the vertices is get readjusted to (y, -x) native (x, y).

Thus, alternative (D) is correct option.


For every allude in the airplane (x, y), a 90° rotation can be explained by the transformation P(x, y) → P"(-y, x). We can accomplish this same revolution by performing two reflections.

A reflection across the heat y = x "swaps" the collaborates of every allude so that every suggest P(x, y) transforms right into a brand-new point P"(y, x). If we follow this with a reflection across the y-axis, we can flip the authorize of our x-coordinate, causing a brand-new point P""(-y, x). Come review:

*
reflectP"(y,x)xrightarrowreflectP""(-y,x)" title="b58ec">

comparing this come the effect of a 90° rotation:

*
rotateP"(-y,x)" title="7aa03">

We deserve to see that the outcomes are identical, so showing a figure throughout the line y = x and then throughout the y-axis is tantamount to rotating that 90° counterclockwise.


If we have given collaborates of the picture are in type (h,k).


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

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

We have the right to see that x-coordinate is gift multiplied by -1 and then y-coordinate is additionally being multiplied by -1.

Above rule could be break into two parts.

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

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

in second step (-h,k) > (-h,-k) is being reflecting over the y-axis.

Therefore, correct choice is C) showing over the x-axis and the y-axis.


Reflecting end the x-axis and also then mirroring over the line y = x.

Step-by-step explanation:

A rotation 90° counterclockwise will certainly map every point (x, y) to (-y, x).

Since the x- and y-coordinates are switched, this is no a reflection across the x-axis adhered to by a reflection throughout the y-axis.

Since the y-coordinate is negated and the x- and y-coordinates are switched, this is not a translation.

Reflecting throughout the x-axis will certainly negate the y-coordinate, giving us (x, -y). Following this v a reflection across y=x will certainly switch the coordinates giving us (-y, x). This is the exactly transformation.


The revolution which is equivalent to rotating a number counterclockwise is showing over the -axis and also -axis. Therefore, the is correct.


Further explanation:

Consider a name: coordinates in the type whereby and are real numbers.

If and are optimistic then the point lies in the very first quadrant.

If we revolve the coordinate counterclockwise climate the coordinates come to be .

The coordinate lies in the third quadrant.

If us reflect the name: coordinates about the -axis then the coordinates become .

The coordinate lies in the 4th quadrant.

If us reflect the name: coordinates about the -axis then the coordinates become .

The coordinate lies in the third quadrant.

This suggests that rotating a number counterclockwise is equivalent to transformation of mirroring over -axis and also reflecting over -axis.

Option (A)

In alternative (A) the is provided that reflection around the heat is identical to rotating a number counterclockwise.

If us reflect the coordinate around the line climate the coordinates come to be .

This is not same as rotating the figure counterclockwise.

Therefore, the alternative (A) is incorrect.

Option (B)

In option (B) that is offered that reflection around is indistinguishable to rotating a number counterclockwise.

If us reflect the name: coordinates around the heat then the coordinates come to be

*
.

This is not very same as rotating the number counterclockwise.

Therefore, the option (B) is incorrect.

Option (C)

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

If us reflect the coordinate about -axis and -axis climate the coordinates end up being .

This is very same as rotating the figure counterclockwise.

Therefore, the option (C) is correct.

Option (D)

In option (D) it is offered that changing a suggest units left and systems down is identical to rotating a figure counterclockwise.

If we change the allude , systems left and also devices down the name: coordinates is .

This is not same as rotating the number counterclockwise.

Therefore, the choice (D) is incorrect.

Therefore, the is correct.

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Learn more

1. Learn an ext about the rotation that the triangle about the origin

2. Learn much more about when a triangle is rotated about the origin

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Geometry

Keywords: Transformation, rotation, reflection, clockwise, geometry, counterclockwise, -axis, - axis, coordinates, graph, origin, line, degrees, translation, symmetry.