Question

determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. then find the scale factor of the dilation.
for each set of triangle vertices, find and graph the coordinates of the vertices of the image after a dilation of the triangle by the given scale factor.

Explanation:

Problem 1 (Rectangle Dilation)

Step1: Identify Corresponding Sides

Left rectangle side: \( 6 \, \text{m} \), Right rectangle side: \( 18 \, \text{in} \)? Wait, units might be mismatched, but assume same shape. Let's take the side of the first rectangle (left) as \( 6 \) (let's say units) and the second (right) as \( 18 \).

Step2: Determine Dilation Type and Scale Factor

Since \( 18 > 6 \), it's an enlargement. Scale factor \( k = \frac{\text{Image Length}}{\text{Original Length}} = \frac{18}{6} = 3 \).

Problem 2 (Triangle Dilation)

Step1: Identify Corresponding Sides

Original triangle side: \( 12 \, \text{cm} \), Image triangle side: \( 6 \, \text{cm} \).

Step2: Determine Dilation Type and Scale Factor

Since \( 6 < 12 \), it's a reduction. Scale factor \( k = \frac{\text{Image Length}}{\text{Original Length}} = \frac{6}{12} = \frac{1}{2} \).

Problem 3 (Hexagon Dilation)

Step1: Identify Corresponding Sides

Original hexagon side: \( 9 \, \text{ft} \), Image hexagon side: \( 6 \, \text{ft} \) (assuming \( YG \) is a typo, maybe \( 6 \, \text{ft} \)).

Step2: Determine Dilation Type and Scale Factor

Since \( 6 < 9 \), it's a reduction. Scale factor \( k = \frac{6}{9} = \frac{2}{3} \).

Problem 4 (Quadrilateral Dilation)

Answer:

s:

1. Rectangle: Enlargement, Scale Factor \( 3 \)
2. Triangle: Reduction, Scale Factor \( \frac{1}{2} \)
3. Hexagon: Reduction, Scale Factor \( \frac{2}{3} \)
4. Quadrilateral: Enlargement, Scale Factor \( \frac{8}{5} \) (or \( 1.6 \))

(Note: Unit mismatches in the problem might be errors, but solved based on given lengths.)