Question

graph the image of parallelogram stuv after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

From graph: \( S(-1,-2) \), \( T(1,-2) \), \( U(1,2) \), \( V(-1,2) \)

Step2: Apply dilation rule

Dilation center origin, scale factor 4: \( (x,y) \to (4x,4y) \)

• \( S' = (4(-1),4(-2)) = (-4,-8) \)
• \( T' = (4(1),4(-2)) = (4,-8) \)
• \( U' = (4(1),4(2)) = (4,8) \)
• \( V' = (4(-1),4(2)) = (-4,8) \)

Step3: Plot image points

Graph \( S'(-4,-8) \), \( T'(4,-8) \), \( U'(4,8) \), \( V'(-4,8) \) and connect.

Answer:

The image of parallelogram \( STUV \) after dilation has vertices \( (-4,-8) \), \( (4,-8) \), \( (4,8) \), \( (-4,8) \). Plot these points to form the dilated parallelogram.