Question

1. (03.01 mc)

triangle efg is dilated by a scale factor of 3 centered at (0, 1) to create triangle efg. which statement is true about the dilation? (1 point)

• $overline{eh}$ and $overline{eh}$ both pass through the center of dilation.
• the slope of $overline{ef}$ is the same as the slope of $overline{eh}$.
• $overline{eg}$ will overlap $overline{eg}$.
• $overline{eh} \cong \overline{eh}$.

Explanation:

Step1: Recall the property of dilation

In a dilation, the line segments connecting corresponding points pass through the center of dilation.

Step2: Analyze each option

• For option 1: Since dilation is centered at \((0,1)\), the line segments \(\overline{EH}\) and \(\overline{E'H'}\) (where \(H'\) is the image of \(H\) after dilation) both pass through the center of dilation \((0,1)\) because of the definition of dilation (all points and their images are collinear with the center of dilation).
• For option 2: The slope of \(\overline{EH}\) and \(\overline{E'H'}\) is not the same. After dilation, the length changes and the orientation (in terms of slope) related to the center of dilation makes the slopes different.
• For option 3: \(\overline{E'G'}\) will not overlap \(\overline{EG}\) as there is a scale - factor of 3 (lengths are different).
• For option 4: \(\overline{EH}

eq\overline{E'H'}\) because of the scale - factor of 3 ( \(E'H' = 3\times EH\)).

Answer:

The first option: \(\overline{EH}\) and \(\overline{E'H'}\) both pass through the center of dilation.