Question

are the triangles similar? explain why or why not.
no, because point j should be at (-3.5, 2) for the two triangles to be similar.
no, because point j should be at (-6, 1.5) for the two triangles to be similar.
yes, because △jkl can be dilated by a scale factor of 1/2 using the origin as the center of dilation and then the image can be rotated 90° counterclockwise with the origin as the center of rotation.
yes, because △jkl can be dilated by a scale factor of 1/3 using the origin as the center of dilation and then the image can be rotated 90° clockwise with the origin as the center of rotation.

Explanation:

Step1: Recall similarity conditions

Two triangles are similar if one can be obtained from the other by dilation and rigid - motions (rotation, translation, reflection).

Step2: Check dilation factor

Count the side - lengths of the triangles. Let's assume the vertices of $\triangle{JKL}$ are $J(-6,4)$, $K(6,4)$, $L(0, - 2)$ and for $\triangle{J'K'L'}$, we can estimate the vertices. If we consider dilation from the origin, we can see that the side - lengths of $\triangle{J'K'L'}$ are about one - third of the side - lengths of $\triangle{JKL}$.

Step3: Check rotation

We can observe that after dilation, a $90^{\circ}$ clock - wise rotation about the origin can map $\triangle{J'K'L'}$ to a position relative to $\triangle{JKL}$.

Answer:

Yes, because $\triangle{JKL}$ can be dilated by a scale factor of $\frac{1}{3}$ using the origin as the center of dilation and then the image can be rotated $90^{\circ}$ clockwise with the origin as the center of rotation.