Answer:
Rectangle ABCD was dilated by [tex]\frac{1}{2}[/tex] followed by a translation of 7 units right and 1 unit down.
Step-by-step explanation:
Rectangle A'B'C'D' is a dilated form of rectangle ABCD.
Followed by a translation, as shown in the figure attached.
For dilation,
Scale factor = [tex]\frac{\text{Side length of image}}{\text{Side length of original}}[/tex]
= [tex]\frac{2}{4}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, rectangle ABCD was dilated with a scale factor of [tex]\frac{1}{2}[/tex] about the origin.
Coordinates of point A → (-10, 6)
Coordinates of point A' → (1, 2)
Coordinates of image of point A after dilation,
(x, y) → (kx, ky)
A(-10, 6) → A"(-5, 3)
Coordinates of point A" after translation of 'h' units to the right and 'k' units down.
(x, y) → (x + h, y - k)
A"(-5, 3) → A'[(-5 + h), (3 - k)]
By comparing the coordinates of A'[(1, 2) and (-5 + h, 3 - k)],
-5 + h = 2 ⇒ h = 7
3 - k = 2 ⇒ k = 1
Therefore, rectangle ABCD was dilated by [tex]\frac{1}{2}[/tex] followed by a translation of 7 units right and 1 unit down.