Question

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

Explanation:

Step1: Identify coordinates of KLMN

First, find the coordinates of each vertex of rectangle \( KLMN \). From the graph:

• \( K(-1, -2) \)
• \( L(1, -2) \)
• \( M(1, 1) \)
• \( N(-1, 1) \)

Step2: Apply dilation (scale factor 4, center origin)

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (kx, ky) \). For \( k = 4 \):

• For \( K(-1, -2) \): \( (4 \times -1, 4 \times -2) = (-4, -8) \)
• For \( L(1, -2) \): \( (4 \times 1, 4 \times -2) = (4, -8) \)
• For \( M(1, 1) \): \( (4 \times 1, 4 \times 1) = (4, 4) \)
• For \( N(-1, 1) \): \( (4 \times -1, 4 \times 1) = (-4, 4) \)

Step3: Plot the new points

Plot the points \( (-4, -8) \), \( (4, -8) \), \( (4, 4) \), and \( (-4, 4) \) on the coordinate plane and connect them to form the dilated rectangle.

Answer:

The dilated rectangle has vertices at \( (-4, -8) \), \( (4, -8) \), \( (4, 4) \), and \( (-4, 4) \). (Graphing these points on the given grid will show the image after dilation.)