Question

May I please get help with the a and b only, and the dilation at the origin? For I am confused as to how I should do the dilation on the graph and find the right answers for a and b. I have tried multiple times but still get them all wrong.

Answer 1

ANSWERS

(a) Shortest side length of the original figure: 1 unit

Shortest side length of the final figure: 3 units

(b) Shortest side length of the final figure = 3 x shortest side length of the original figure.

EXPLANATION

A dilation with center at the origin (0, 0) and scale factor k, follows this rule for every point (x, y):

$(x,y)\to(kx,ky)$

In this case, the scale factor is 3, so we have to multiply both coordinates of each vertex by 3 to obtain the dilated figure,

Note that each point of each figure must be aligned with a line passing through the origin.

(a) The shortest side of the original figure is the one on the right of the figure, and it is 1 unit long. Note that for both figures, the shortest side is in the same position, so the shortest side of the final figure is 3 units long.

(b) We can conclude from part a - and from the diagram, that after a dilation with a scale factor of 3, each side of the final figure is 3 times its corresponding sides of the original figure.