Question

the figure below was made with a scale of 1 unit = 8 cm. draw the figure with a new scale of 1 unit = 2 cm. you can place your figure anywhere on the grid on the right.

Explanation:

Step1: Find scaling factor

First, calculate the ratio of the new scale to the old scale:
$\text{Scaling factor} = \frac{\text{New scale per unit}}{\text{Old scale per unit}} = \frac{2\ \text{cm/unit}}{8\ \text{cm/unit}} = \frac{1}{4}$
This means each side length of the original figure will be multiplied by 4 to get the length in the new scale grid (because 1 unit in the new grid represents a smaller real-world length, so the figure will be larger on the grid).

Step2: Measure original figure

The original rectangle on the left grid is 1 unit wide and 1 unit tall (using the 1 unit = 8 cm scale).

Step3: Calculate new dimensions

Multiply each original dimension by the reciprocal of the scaling factor (since we are converting grid units, not real length):
New width = $1 \times \frac{8}{2} = 4$ grid units
New height = $1 \times \frac{8}{2} = 4$ grid units

Step4: Draw the new figure

On the right grid (1 unit = 2 cm), draw a rectangle that is 4 grid units wide and 4 grid units tall, placed anywhere on the grid.

Answer:

Draw a 4-unit by 4-unit rectangle on the right (new scale) grid.