Question

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

Answer 1

Answer:

translation 2 units left ; reflection across the y-axis

Step-by-step explanation:

The y-coordinates of the points do not change from the pre-image to the image.  This means there is no translation down (this would add or subtract to the y-coordinates) and no reflection across the x-axis (this would negate the y-coordinates).

This leaves us with a translation 2 units left and a reflection across the y-axis.

The translation 2 units left adds 2 to the x-coordinates, and the reflection across the y-axis negates the x-coordinates.  If we add 2 first, the coordinates would be (-4+2, 6) = (-2, 6); (-2+2, 2) = (0, 2); and (-6+2, 2) = (-4, 2).

Negating each of these would give us (2, 6); (0, 2); and (4, 2).  These are the desired image coordinates.

Answer 2

Answer-

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