The dashed-lined figure is a dilation image of the solid-lined figure. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?
The figure shows a coordinate grid from negative 10 to 10 on both x and y axes. A solid trapezoid is graphed in the corner of a larger trapezoid.
The solid trapezoid has vertices at
left parenthesis negative 2 comma negative 1 right parenthesis and
left parenthesis negative 2 comma 1 right parenthesis and
left parenthesis 0 comma 1 right parenthesis and
left parenthesis 2 comma negative 1 right parenthesis.
The dashed trapezoid has vertices at
left parenthesis negative 2 comma negative 1 right parenthesis and
left parenthesis negative 2 comma 5 right parenthesis and
left parenthesis 4 comma 5 right parenthesis and
left parenthesis 10 comma negative 1 right parenthesis.
(1 point)
Responses
6; enlargement
6; enlargement
3; enlargement
3; enlargement
3; reduction
3; reduction
one-third; reductio
The dilation is an enlargement. The scale factor of the dilation is 6.
To determine if the dilation is an enlargement or a reduction, we can compare the lengths of corresponding sides of the solid-lined and dashed-lined figures.
First, let's compare the length of the horizontal side (the base) of the trapezoid. The base of the solid-lined trapezoid has a length of 4 units (from -2 to 2), and the base of the dashed-lined trapezoid has a length of 12 units (from -2 to 10).
Since the length of the base of the dashed-lined trapezoid is greater than the length of the base of the solid-lined trapezoid, we can conclude that the dilation is an enlargement.
To find the scale factor of the dilation, we can take the ratio of the lengths of corresponding sides.
The length of the base of the dashed-lined trapezoid is 12 units and the length of the base of the solid-lined trapezoid is 4 units.
So, the scale factor of the dilation is 12/4, which simplifies to 3.
Therefore, the dilation is an enlargement, and the scale factor is 3.
To determine whether the dilation is an enlargement or a reduction, we need to compare the sizes of the corresponding sides of the solid trapezoid and the dashed trapezoid.
Looking at the solid trapezoid, we can see that the height (distance between the top and bottom bases) is 2 units (from -1 to 1). The length of the top base is 4 units (from -2 to 2), and the length of the bottom base is also 4 units.
Now let's compare these measurements to the dashed trapezoid. The height is 6 units (from -1 to 5), the length of the top base is 6 units (from -2 to 4), and the length of the bottom base is 12 units (from -2 to 10).
Since the corresponding sides of the dashed trapezoid are larger than those of the solid trapezoid, we can conclude that the dilation is an enlargement.
To find the scale factor of the dilation, we can compare the corresponding lengths of any side in both trapezoids. Let's take the length of the top bases. In the solid trapezoid, the length is 4 units, and in the dashed trapezoid, it is 6 units.
To find the scale factor, we can divide the length of the dashed trapezoid side by the length of the corresponding side in the solid trapezoid:
Scale factor = Length of dashed trapezoid top base / Length of solid trapezoid top base
Scale factor = 6 units / 4 units
Scale factor = 3/2
Therefore, the scale factor of the dilation is 3/2 or 1.5.