2. Draw the image of ∆ABC under the dilation with scale factor 4 and center of dilation (-3, -4).
List the coordinates for A’, B’, and C’, label the image ∆A’B’C’ on the grid below, and draw in the lines for the sides of A’B’C.

Please note that plotting the image of points on a coordinate plane where center is NOT the origin, can be done by observing the horizontal distances on x-axis and vertical distances on y-axis of each vertex from the center of dilation.

Let us consider the triangle ∆ABC with the sample coordinates A (-4, -6), B (3, -6), and C (-2, -1) and dilated by a scale factor of 4 with a center of dilation at (-3, -4).

Analyzing the dilation of A (-4, -6) with scale factor 4 and center of dilation (-3, -4):

By observation, point A is 2 vertical units down the center of dilation. Under a scale factor of 4, point A' needs to be 8 vertical units from the center.

Also, point A is 1 horizontal unit left of the center of dilation. Point A' needs to be 4 horizontal units left of the center.

So, the new coordinates of the image A' will be (-7, -12). Please check the attached diagram to visualize the dilation.

Analyzing the dilation of B (3, -6) with scale factor 4 and center of dilation (-3, -4):

By observation, point B is 2 vertical units down the center of dilation. Under a scale factor of 4, point A' needs to be 8 vertical units from the center.

Also, point B is 6 horizontal units right of the center of dilation. Point B' needs to be 24 horizontal units right of the center.

So, the new coordinates of the image B' will be (21, -12). Please check the attached diagram to visualize the dilation.

Analyzing the dilation of C (-2, -1) with scale factor 4 and center of dilation (-3, -4):

By observation, point C is 3 vertical units up the center of dilation. Under a scale factor of 4, point C' needs to be 12 vertical units from the center.

Also, point C is 1 horizontal unit right of the center of dilation. Point C' needs to be 4 horizontal units right of the center.

So, the new coordinates of the image C' will be (1, 8). Please check the attached diagram to visualize the dilation.

Hope you understand the concept.

Keywords: dilation, transformation

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2. Draw the image of ∆ABC under the dilation with scale factor 4 and center of dilation (-3, -4). List the coordinates for A’, B’, and C’, label the image ∆A’B’C’ on the grid below, and draw in the lines for the sides of A’B’C.

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2. Draw the image of ∆ABC under the dilation with scale factor 4 and center of dilation (-3, -4).
List the coordinates for A’, B’, and C’, label the image ∆A’B’C’ on the grid below, and draw in the lines for the sides of A’B’C.