Question

figure j, the large hexagon, was dilated with the origin as the center of dilation to create figure k, the small hexagon. decide whether each statement about this dilation is true or false. use the checkmarks to select the correct answer in each row. statement: a scale factor of 5 was applied to figure j to create figure k. true false. statement: if (x, y) represents a point on figure j, then the ordered pair (0.5x, 0.5y) represents the corresponding point on figure k. true false.

Explanation:

Step1: Analyze the first statement

To find the scale factor, we can compare corresponding side lengths or coordinates. Let's take a point on Figure J and its corresponding point on Figure K. For example, a point on Figure J: let's take the rightmost point of Figure J, which is at (6, 0). The corresponding point on Figure K is at (3, 0). The scale factor \( k \) is calculated as \( k=\frac{\text{coordinate of K}}{\text{coordinate of J}}=\frac{3}{6} = 0.5\). So a scale factor of 5 was not applied (since 0.5 is the scale factor, and it's a reduction, so scale factor less than 1). Thus, the first statement is false.

Step2: Analyze the second statement

When a figure is dilated with the origin as the center of dilation with a scale factor \( k \), the transformation rule is \((x,y)\to(kx,ky)\). We found the scale factor \( k = 0.5\) (or \(\frac{1}{2}\)). So if \((x,y)\) is on Figure J, the corresponding point on Figure K should be \((0.5x, 0.5y)\) (since \( k = 0.5\)). Thus, the second statement is true.

Answer:

• Statement: "A scale factor of 5 was applied to Figure J to create Figure K." → False (check the "False" box)
• Statement: "If \((x, y)\) represents a point on Figure J, then the ordered pair \((0.5x, 0.5y)\) represents the corresponding point on Figure K." → True (check the "True" box)