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Triangle ABC is reflected across the x-axis, and then across the y-axis. Which rotation is equivalent to this composition of transformations?
A) 45 degree rotation
Eliminate
B) 90 degree rotation
C) 180 degree rotation
D) 360 degree rotation

Triangle ABC is reflected across the xaxis and then across the yaxis Which rotation is equivalent to this composition of transformations A 45 degree rotation E class=

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InesWalston

Answer:

C) 180 degree rotation

Step-by-step explanation:

While reflecting a point, with coordinates as (x, y), over x axis the new co-ordinates become (x, -y)

⇒(x, y) → (x, -y)

While reflecting a point, with coordinates as (x, y), over y axis the new co-ordinates become (-x, y)

⇒(x, y) → (-x, y)

So, when these two operations are combined, they the rule followed is,

⇒(x, y) → (-x, -y)

We also know that while rotating a point, with coordinates as (x, y), 180° the new co-ordinates become (-x, -y)

⇒(x, y) → (-x, -y)

Therefore, reflecting a point over x axis and then over y axis will yield the same result as rotating a point 180°.

[tex]\boxed{180{\text{ degree rotation}}}[/tex] is equivalent to this composition of transformations.

Further explanation:

Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.

Rotation is defined as a movement around its own axis. A circular movement is a rotation.

Given:

The options are as follows,

(A). 45 degree rotation

(B). 90 degree rotation

(C). 180 degree rotation

(D). 360 degree rotation

Explanation:

The angle in the first quadrant is [tex]{0^ \circ }[/tex] to [tex]{90^ \circ }.[/tex]

The angle in the second quadrant is [tex]{90^ \circ }[/tex] to [tex]{180^ \circ }.[/tex]

The angle in the third quadrant is [tex]{180^ \circ }[/tex] to [tex]{270^ \circ }.[/tex]

The angle in the fourth quadrant is [tex]{270^ \circ }[/tex] to [tex]{360^ \circ }.[/tex]

If we rotate the triangle [tex]{90^ \circ}[/tex] anticlockwise the triangle will go in the fourth quadrant and if we again rotate [tex]{90^ \circ}[/tex] anticlockwise the triangle will go in the third quadrant.

The total rotation is of [tex]{180^ \circ }.[/tex]

[tex]\boxed{180{\text{ degree rotation}}}[/tex] is equivalent to this composition of transformations.

Option (A) is not correct as the 45 degree rotation is not equivalent to this composition of transformations.

Option (B) is not correct as the 90 degree rotation is not equivalent to this composition of transformations.

Option (C) is correct as the 180 degree rotation is equivalent to this composition of transformations.

Option (D) is not correct as the 360 degree rotation is not equivalent to this composition of transformations.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: rotation, translation, reflection, x-axis, y-axis, equivalent composition, degree rotation,  triangle, rotation about point A, triangle pair, equal angles, sides, congruent, two triangles, common point.