The coordinates of a rectangle are (4, 0), (8, 0), (4, 10) and (8, 10). Which transformation results in a reduction in the size of a rectangle?
a
The rectangle reflects across the y-axis.
b
The rectangle undergoes a dilation by a scale factor of 2.
c
The rectangle translates 3 units to the left and 6 units up.
d
The rectangle undergoes a dilation by a scale factor of 0.5.
d
The rectangle undergoes a dilation by a scale factor of 0.5.
To determine which transformation results in a reduction in the size of a rectangle, we need to understand what each transformation does.
a) Reflecting across the y-axis swaps the x-coordinates of all points. It does not change the size of the rectangle, only its position.
b) Dilation by a scale factor of 2 increases the size of the figure. It stretches the rectangle horizontally and vertically.
c) Translating 3 units to the left and 6 units up moves the entire rectangle without changing its size.
d) Dilation by a scale factor of 0.5 decreases the size of a figure. It shrinks the rectangle horizontally and vertically.
Comparing these transformations to the given rectangle, we determine that the correct answer is (d) - the rectangle undergoes a dilation by a scale factor of 0.5. This will result in a reduced size of the rectangle.
d
The rectangle undergoes a dilation by a scale factor of 0.5.