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

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

2. Enlargement

Step-by-step 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.