Question

is efgh similar to lmno? justify your answer.
yes, because a dilation by a scale factor of \\( \frac { 1 } { 2 } \\) centered at point h maps efgh onto lmno.
yes, because a dilation by a scale factor of \\( \frac { 1 } { 2 } \\) centered at the origin maps efgh onto lmno.

Explanation:

Step1: Recall the property of similar figures

Similar figures can be obtained by dilation. Dilation is a transformation that changes the size of a figure but not its shape.

Step2: Analyze the scale factor and center of dilation

If we consider the coordinates of the vertices of \(EFGH\) and \(LMNO\). Let's assume we check the distance between corresponding vertices. For example, if we take a vertex of \(EFGH\) and the corresponding vertex of \(LMNO\) (after proper identification). A dilation centered at the origin with a scale factor \(k=\frac{1}{2}\) maps \(EFGH\) onto \(LMNO\) because if we consider the general rule of dilation \((x,y)\to(kx,ky)\) for a dilation centered at the origin.

Answer:

Yes, because a dilation by a scale factor of \(\frac{1}{2}\) centered at the origin maps \(EFGH\) onto \(LMNO\).