Question

1. draw a reduction of this pentagon using a scale factor of 3:4.

Explanation:

Step1: Measure original side lengths

First, count grid units for each side:

• Top/bottom straight sides: 6 units
• Left vertical side: 4 units
• Two slanted sides: each spans 2 horizontal, 2 vertical units (length $2\sqrt{2}$ units)

Step2: Apply scale factor $\frac{3}{4}$

Multiply each length by the scale factor:

• Scaled straight horizontal sides: $6 \times \frac{3}{4} = 4.5$ units
• Scaled vertical side: $4 \times \frac{3}{4} = 3$ units
• Scaled slanted sides: $2\sqrt{2} \times \frac{3}{4} = 1.5\sqrt{2}$ units (spans 1.5 horizontal, 1.5 vertical units)

Step3: Draw scaled pentagon

1. Draw a vertical side of 3 units.
2. Attach a 4.5-unit horizontal side to its top/bottom.
3. From the end of the horizontal side, draw two slanted segments (each 1.5 horizontal, 1.5 vertical units) that meet at a point to form the notched end, connecting back to the bottom/top of the vertical side.

Answer:

A reduction of the pentagon where all linear dimensions are $\frac{3}{4}$ of the original:

• Vertical side: 3 grid units
• Horizontal straight sides: 4.5 grid units
• Slanted sides: each spans 1.5 horizontal and 1.5 vertical grid units, forming the notched end. When drawn, the shape retains the original pentagon's proportions but is smaller by the scale factor $\frac{3}{4}$.