Question

graph the image of parallelogram qrst after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of \( Q, R, S, T \) from the graph.

• \( Q(-2, -2) \)
• \( R(0, -2) \)
• \( S(2, -1) \)
• \( T(0, -1) \)

Step2: Apply dilation rule

Dilation centered at the origin with scale factor \( k \) transforms a point \( (x, y) \) to \( (kx, ky) \). Here, \( k = 5 \).

• For \( Q(-2, -2) \): \( (5 \times -2, 5 \times -2) = (-10, -10) \)
• For \( R(0, -2) \): \( (5 \times 0, 5 \times -2) = (0, -10) \)
• For \( S(2, -1) \): \( (5 \times 2, 5 \times -1) = (10, -5) \)
• For \( T(0, -1) \): \( (5 \times 0, 5 \times -1) = (0, -5) \)

Step3: Graph the new points

Plot \( Q'(-10, -10) \), \( R'(0, -10) \), \( S'(10, -5) \), \( T'(0, -5) \) and connect them to form the dilated parallelogram.

Answer:

The dilated parallelogram has vertices at \( Q'(-10, -10) \), \( R'(0, -10) \), \( S'(10, -5) \), \( T'(0, -5) \) (graph by plotting these points and connecting them).