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; reduction
To determine whether the dilation is an enlargement or a reduction, we should compare the sizes of the solid-lined and dashed-lined trapezoids. The solid trapezoid appears to be smaller than the dashed trapezoid, suggesting that the dilation is an enlargement.
Now, let's calculate the scale factor of the dilation by comparing the corresponding vertices of the two trapezoids. We can use either the vertical side or the horizontal side to find the scale factor.
For the vertical side:
The solid trapezoid has a height determined by the y-coordinates of its vertices (1 - (-1) = 2 units).
The dashed trapezoid has a height determined by the y-coordinates of its vertices (5 - (-1) = 6 units).
The scale factor k can be found by dividing the height of the dashed trapezoid by the height of the solid trapezoid: k = 6 / 2 = 3.
So, the scale factor is 3, which corresponds to an enlargement (since k > 1).
Therefore, the correct response is "3; enlargement."