Triangle L'M'N' is a dilation of triangle LMN. If the scale factor of the dilation is 1/5, which of the following statements is true?

Triangle L'M'N' is a rotation of triangle LMN.

Triangle L'M'N' is the same size as triangle LMN.

Triangle L'M'N' is a reduction of triangle LMN.

Triangle L'M'N' is an enlargement of triangle LMN.

1/5 scale is a reduction

answer is a

To determine which of the given statements is true, let's first understand what a dilation is.

A dilation is a transformation that changes the size of a figure while keeping the shape the same. It is performed by multiplying the coordinates of each point in the original figure by a scale factor.

In this case, the scale factor is given as 1/5. This means that every coordinate of triangle LMN has to be multiplied by 1/5 to get the corresponding coordinate of triangle L'M'N'.

Now, let's analyze each statement:

1. Triangle L'M'N' is a rotation of triangle LMN.
A rotation is a transformation that rotates a figure around a fixed point. Since a dilation only changes the size of the figure, but not its shape or orientation, this statement is NOT true.

2. Triangle L'M'N' is the same size as triangle LMN.
Since the scale factor is 1/5, every coordinate of triangle LMN is multiplied by 1/5 to get the coordinates of triangle L'M'N'. Therefore, the sides of triangle L'M'N' will be 1/5th the length of the sides of triangle LMN. So, this statement is NOT true.

3. Triangle L'M'N' is a reduction of triangle LMN.
A reduction occurs when the scale factor is less than 1, which is the case here (1/5). The reduction means that the size of triangle L'M'N' is smaller compared to triangle LMN. Hence, this statement is TRUE.

4. Triangle L'M'N' is an enlargement of triangle LMN.
An enlargement occurs when the scale factor is greater than 1. In this case, the scale factor is 1/5, which is less than 1, so this statement is NOT true.

Therefore, the correct statement is: Triangle L'M'N' is a reduction of triangle LMN.

Triangle L'M'N' is an enlargement of triangle LMN.