Question

The coordinates of the vertices of △ABC are A(−4, 6) , B(−2, 2) , and C(−6, 2) .

The coordinates of the vertices of △A′B′C′ are A′(2, 6) , B′(0, 2) , and C′(4, 2) .



Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △ABC to △A′B′C′ is a blank followed by a blank.
translation 2 units left
reflection across the x-axis
reflection across the y-axis
translation 2 units down

Answer 1

Here is my test answer

Explanation:

Answer 2

The sequences of transformations that maps △ABC to △A′B′C′ are

1. Reflection across the y-axis
2. Translation 2 units left

Solution-

The coordinates of the vertices of ΔABC are

A = (−4, 6)

B = (−2, 2)

C = (−6, 2)

The coordinates of the vertices of ΔA′B′C′ are

A′ = (2, 6)

B′ = (0, 2)

C′ = (4, 2)

As all the y-coordinates of all the function are same, so the triangle is neither translated up or down (∵ (x, y) → (x, y±k)), nor reflected over x-axis(∵ (x, y) → (x, -y)).

As the signs of x-coordinate is changed, it might be reflected over y axis,

Rule for reflection over y axis is,

(x, y) → (-x, y)

so,

A" = (4, 6)

B" = (2, 2)

C" = (6, 2)

As the x-coordinates of vertices of ΔA′B′C′ are 2 units less than that of ΔA"B"C"

So it is then translated 2 units left.

Therefore, the sequences of transformations that maps △ABC to △A′B′C′ are

1. Reflection across the y-axis
2. Translation 2 units left