Question

Rectangle ABCD is transformed into rectangle A'B'C'D' by the following sequence of transformations. First, the figure is translated 5 units to the right and 3 units down, and then it is reflected across the y-axis. Finally, it is dilated by a scale factor of one-half.

After the transformation, point A' is located at (___ , ___).

Answer 1

A'(-1/2, 0)

Explanation:

Translation right 5 and down 3 is ...

(x, y) ⇒ (x +5, y -3)

Reflection across the y-axis negates the x-coordinate:

(x, y) ⇒ (-x, y)

Dilation by a scale factor of 1/2 multiplies each coordinate by 1/2:

(x, y) ⇒ (x/2, y/2)

Together these three transformations give ...

(x, y) ⇒ (-(x +5)/2, (y -3)/2)

__

The point A(-4, 3) gets transformed to ...

A(-4, 3) ⇒ A'(-(-4+5)/2, (3-3)/2) = A'(-1/2, 0)

_____

Additional comment

The remaining points of the figure get transformed as follows:

B(5, 3) ⇒ B'(-(5 +5)/2, (3 -3)/2) = B'(-5, 0)

C(5, -2) ⇒ C'(-(5+5)/2, (-2-3)/2) = C'(-5, -5/2)

D(-4, -2) ⇒ D'(-(-4+5)/2, (-2-3)/2) = D'(-1/2, -5/2)