Question

A triangle is shown. The table names different transformations that can be applied to the triangle.

Answer 1

The given transformations are rigid transformation in which the image

can be located by a formula.

Response:

First reflect across the x-axis then reflect across the y-axis

• Figure: Second graph

First, rotate 180° counterclockwise around the origin. Then reflect across the x-axis.

• Figure: Third graph

First translate 9 units to the left. Then reflect across the x-axis

• Figure: First graph

Which method is used to determine the transformation of an image?

The coordinates of (x, y) following a reflection across the x-axis is (x, -y)

The coordinates following a reflection across the y-axis is (-x, y)

The points of the triangle following the first transformation is therefore;

(4, 4) → (4, -4) → (-4, -4)

(8, 4) → (8, -4) → (-8, -4)

(6, 6) → (6, -6) → (-6, -6)

The image from the first transformation is (-4, -4), (-8, -4), (-6, -6), which

corresponds to the second graph.

The coordinates following a rotation of (x, y) by 180° about the origin is (-x, -y)

A reflection of the point (-x, -y) about the x-axis is (-x, y).

Therefore;

(4, 4) → (-4, -4) → (-4, 4)

(8, 4) → (-8, -4) → (-8, 4)

(6, 6) → (-6, -6) → (-6, 6)

The image from the second transformation is (-4, 4), (-8, 4), (-6, 6), which corresponds to the third graph.

The coordinates following a translation of 9 units to the left is (x - 9, y)

A reflection of the point (x - 9, y) about the x-axis is (x - 9, -y)

Therefore;

(4, 4) → (4 - 9, -4) = (-5, -4)

(8, 4) → (8 - 9, -4) = (-1, -4)

(6, 6) → (6 - 9, -6) → (-3, -6)

The image from the third transformation is (-13, -9), (-1, -4), (-7, -6), which corresponds to the first graph.

Learn more about rigid transformations here:

brainly.com/question/11408409

Answer 2

this  would be a reflection

Step-by-step explanation:

I know this because reflections are like this

1) over the x axis- change the y

2) over y axis - change sign on x

3) flip over a line of reflection