Question

the trapezoid hijk is a dilation of the trapezoid hijk. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find coordinates of original and dilated points

Original trapezoid \( HIJK \): Let's take points \( H( -1, 2) \), \( I( -2, 2) \), \( J( -2, -1) \), \( K(2, -1) \) (approximate from graph). Dilated trapezoid \( H'I'J'K' \): \( H'(-4, 8) \), \( I'(-8, 8) \), \( J'(-8, -4) \), \( K'(8, -4) \).

Step2: Calculate scale factor using coordinates

Scale factor \( k \) is the ratio of corresponding coordinates. For point \( H \) to \( H' \): \( x \)-coordinate: \( \frac{-4}{-1} = 4 \), \( y \)-coordinate: \( \frac{8}{2} = 4 \). Check another point, e.g., \( K \) to \( K' \): \( x \)-coordinate: \( \frac{8}{2} = 4 \), \( y \)-coordinate: \( \frac{-4}{-1} = 4 \). So scale factor is 4.

Answer:

4