Question

The coordinates of triangle CDE are as follows:The triangle is dilated by a scale factor of 3.1. What are the new coordinates of triangle C'D'E'?2. Is this an enlargement, congruency, or a reduction? Explain.C (3,5)D (7,5)E (5,2)

Answer 1

ANSWER

1. C'(9, 15), D'(21, 15), E'(15, 6)

2. Enlargement

EXPLANATION

Assuming the center of dilation is the origin, the rule to find the image of each point on the figure after dilation by a scale factor of 3 is,

$(x,y)\rightarrow(3x,3y)$

So, the vertices of the triangle have the images,

$\begin{gathered} C(3,5)\rightarrow C^{\prime}(9,15) \\ D(7,5)\rightarrow D^{\prime}(21,15) \\ E(5,2)\rightarrow E^{\prime}(15,6) \end{gathered}$

The triangle obtained is larger than the triangle CDE. This is because the scale factor is a value greater than 1, so it produces a larger image.

If the scale factor is between 0 and 1, it produces a smaller image and, if it is equal to 1, the image produced is congruent to the pre-image.

Hence, the coordinates of triangle C'D'E' are C'(9, 15), D'(21, 15), E'(15, 6), and the dilation is an enlargement.