Question

the graph shows triangles abc and jkl. are abc and jkl similar? yes, because a dilation centered at the origin with a scale factor of 2 followed by a translation two units to the left and one unit up maps abc onto jkl. yes, because a dilation centered at the origin with a scale factor of 1/2 followed by a translation two units to the right and one unit down maps abc onto jkl. yes, because a translation one unit to the left followed by a dilation centered at the origin with a scale factor of 2 maps abc onto jkl. no, because there is no sequence of translations, rotations, reflections, and dilations that maps abc onto jkl.

Explanation:

Step1: Recall similarity criteria

Similar triangles can be obtained by a sequence of rigid - motions (translations, rotations, reflections) and dilations.

Step2: Analyze dilation and translation

If we consider a dilation centered at the origin with a scale factor of $\frac{1}{2}$, the coordinates of the vertices of $\triangle ABC$ will be shrunk. Then, a translation two units to the right and one unit down will map the dilated triangle onto $\triangle JKL$.

Answer:

Yes, because a dilation centered at the origin with a scale factor of $\frac{1}{2}$ followed by a translation two units to the right and one unit down maps $ABC$ onto $JKL$.