Final answer:
To graph △LMN and its image after a dilation centered at the origin with scale factor k= -3, plot the given vertices L(0, 0), M(-4, 1), and N(-3, -6) on a coordinate plane. Then, multiply the coordinates of each vertex by the scale factor -3 to find the coordinates of the image. Finally, connect the three images of the vertices to obtain the graph of the dilated triangle △L'M'N'.
Step-by-step explanation:
To graph △LMN and its image after a dilation centered at the origin with scale factor k= -3, we first plot the given vertices L(0, 0), M(-4, 1), and N(-3, -6) on a coordinate plane. Then, we multiply the coordinates of each vertex by the scale factor -3 to find the coordinates of the image. The image of L is (0, 0), the image of M is (-4 * -3, 1 * -3) = (12, -3), and the image of N is (-3 * -3, -6 * -3) = (9, 18). Connecting the three images of the vertices will give us the graph of the dilated triangle △L'M'N'.