Question

Arachne's Quilt is an Amish quilt pattern made of polygons. You can use a coordinate plane to plan a quilt. Graph a pentagon with the vertices A(8,0), B(6,-2), C(6, -6), D(4, -4), and E(4,0). Then to graph another pentagon, follow these steps.

1. Translate pentagon ABCDE 4 units to the left to form pentagon A'B'C'D'E'.
2. Rotate pentagon A'B'C'D'E' 90° counterclockwise around the origin to form pentagon A' 'B' 'C' 'D' 'E''.

Is pentagon A' 'B' 'C' 'D' E'' the same size and shape as pentagon ABCDE?

Answer 1

To graph the pentagon ABCDE, plot the given points on a coordinate plane. Then, translate and rotate the pentagon to form pentagon A''B''C''D''E''. The two pentagons are the same size and shape.

Step-by-step explanation:

To graph pentagon ABCDE, plot the given points on a coordinate plane:

• A(8,0)
• B(6,-2)
• C(6,-6)
• D(4,-4)
• E(4,0)

Then, to translate the pentagon 4 units to the left, subtract 4 from the x-coordinates of each point:

• A'(8-4,0) = A'(4,0)
• B'(6-4,-2) = B'(2,-2)
• C'(6-4,-6) = C'(2,-6)
• D'(4-4,-4) = D'(0,-4)
• E'(4-4,0) = E'(0,0)

To rotate pentagon A'B'C'D'E' 90° counterclockwise around the origin, switch the x-coordinates with the y-coordinates and negate the new x-coordinates:

• A''(-0,4) = A''(0,4)
• B''(-2,2) = B''(2,-2)
• C''(-6,2) = C''(2,-6)
• D''(-4,0) = D''(0,-4)
• E''(0,0) = E''(0,0)

Pentagon A''B''C''D''E'' is the same size and shape as pentagon ABCDE.