Question

a square has a perimeter of 96 units. create a scale drawing of the square using a scale factor of \\(\frac{1}{4}\\). start at the point (0, 0)

Explanation:

Step1: Find side length of original square

A square's perimeter \( P = 4s \), where \( s \) is side length. Given \( P = 96 \), solve for \( s \):
\( 4s = 96 \)
\( s = \frac{96}{4} = 24 \) units.

Step2: Apply scale factor to find scaled side length

Scale factor is \( \frac{1}{4} \). Scaled side length \( s' = 24 \times \frac{1}{4} = 6 \) units.

Step3: Determine coordinates for scale drawing

Start at \( (0, 0) \). A square has 4 sides, so the vertices (in order) will be:

• \( (0, 0) \) (start)
• \( (6, 0) \) (right along x - axis)
• \( (6, 6) \) (up along y - axis)
• \( (0, 6) \) (left along x - axis)
• Back to \( (0, 0) \) (down along y - axis)

To draw the square, plot these points and connect them. The side length of the scaled square is 6 units, so from \( (0,0) \), move 6 units right to \( (6,0) \), 6 units up to \( (6,6) \), 6 units left to \( (0,6) \), and back to \( (0,0) \).

Answer:

The scale - drawn square has vertices at \((0,0)\), \((6,0)\), \((6,6)\), \((0,6)\) (and back to \((0,0)\)) with a side length of 6 units.