Question

1. rectangle wxyz has a perimeter of 30 units. determine which ordered pairs could be the coordinates of points y and z.

select all that apply.

□ y(-3, 7) and z(6, 7)
□ y(1, -6) and z(1, 3)
□ y(6, 7) and z(-3, 7)
□ y(6, -5) and z(-3, -5)
□ y(6, -6) and z(-3, -6)
□ y(-3, 7) and z(6, -5)

Explanation:

First, find the length of \( WX \). From the graph, \( W \) is at \( (-3, 1) \) and \( X \) is at \( (6, 1) \), so the length of \( WX \) is \( |6 - (-3)| = 9 \) units.

For a rectangle, the perimeter \( P = 2(l + w) \), where \( l \) is length and \( w \) is width. Given \( P = 30 \), we can find the width:

Step1: Find the width

\( 30 = 2(9 + w) \)
Divide both sides by 2: \( 15 = 9 + w \)
Subtract 9: \( w = 6 \) units.

Now, check each option for the length of \( YZ \) (which should be equal to \( WX = 9 \)) and the length of \( XY \) (which should be equal to the width \( 6 \)) or \( WZ \) (same as \( XY \)).

Option 1: \( Y(-3, 7) \) and \( Z(6, 7) \)

Length of \( YZ \): \( |6 - (-3)| = 9 \) (same as \( WX \)). The vertical distance between \( Y \) (or \( Z \)) and \( W \) (or \( X \)): \( |7 - 1| = 6 \) (width). So this works.

Option 2: \( Y(1, -6) \) and \( Z(1, 3) \)

Length of \( YZ \): \( |3 - (-6)| = 9 \) (vertical length). The horizontal distance between \( Y \) (or \( Z \)) and \( W \) (or \( X \)): \( |1 - (-3)| = 4 \) (not 6) or \( |1 - 6| = 5 \) (not 6). So this does not work.

Option 3: \( Y(6, 7) \) and \( Z(-3, 7) \)

Length of \( YZ \): \( |6 - (-3)| = 9 \) (same as \( WX \)). Vertical distance: \( |7 - 1| = 6 \) (width). Works (same as option 1, just reversed).

Option 4: \( Y(6, -5) \) and \( Z(-3, -5) \)

Length of \( YZ \): \( |6 - (-3)| = 9 \) (same as \( WX \)). Vertical distance: \( |-5 - 1| = 6 \) (width). Works.

Option 5: \( Y(6, -6) \) and \( Z(-3, -6) \)

Length of \( YZ \): \( |6 - (-3)| = 9 \) (same as \( WX \)). Vertical distance: \( |-6 - 1| = 7 \) (not 6). Does not work.

Option 6: \( Y(-3, 7) \) and \( Z(6, -5) \)

Length of \( YZ \): \( \sqrt{(6 - (-3))^2 + (-5 - 7)^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \) (not 9). Does not work.

Answer:

• \( Y(-3, 7) \) and \( Z(6, 7) \)
• \( Y(6, 7) \) and \( Z(-3, 7) \)
• \( Y(6, -5) \) and \( Z(-3, -5) \)