Question

homework ~ unit 1 lesson 3: scale drawing
3.) here is an original figure. draw a scaled copy using a scale factor of 2.
grid with a trapezoid figure
partially visible text: ... using a scale factor of ¼.

Explanation:

Step1: Analyze the original figure

The original figure is a trapezoid. Let's identify the lengths of its sides (in terms of grid units). The top base: let's say it spans 3 grid units (from x - coordinate of the left - top vertex to the right - top vertex). The bottom base: spans 4 grid units (from x - coordinate of the left - bottom vertex to the right - bottom vertex). The height (vertical side) spans 4 grid units (from y - coordinate of the bottom vertices to the top vertices). The slant side: we can calculate its length using the grid, but for scaling, we just need to scale each side by the scale factor.

Step2: Apply the scale factor of 2

To create a scaled copy with a scale factor of 2, we multiply the length of each side by 2.

• New top base length: \(3\times2 = 6\) grid units.
• New bottom base length: \(4\times2=8\) grid units.
• New height (vertical side): \(4\times2 = 8\) grid units.
• The slant side: if the horizontal component of the slant side (in the original) is \(1\) grid unit (from the left - top vertex to the point directly above the left - bottom vertex) and the vertical component is \(4\) grid units, then the new horizontal component is \(1\times2 = 2\) grid units and the new vertical component is \(4\times2=8\) grid units.

Step3: Draw the scaled trapezoid

Start by plotting the bottom - left vertex of the scaled trapezoid. Then, move 8 grid units to the right for the bottom - right vertex (since the new bottom base is 8 units). Then, move 8 grid units up from the bottom - right vertex for the top - right vertex (since the height is 8 units). Then, from the top - right vertex, move 6 grid units to the left for the top - left vertex. Then, connect the top - left vertex to the bottom - left vertex with a line that has a horizontal component of 2 units and a vertical component of 8 units (to match the scaled slant side).

Answer:

To draw the scaled copy:

1. Identify the vertices of the original trapezoid.
2. Multiply the horizontal and vertical distances of each vertex from a reference point (e.g., the bottom - left vertex) by 2.
3. Plot the new vertices using the scaled distances and connect them to form the scaled trapezoid. The scaled trapezoid will have a bottom base of 8 grid units, a top base of 6 grid units, a height of 8 grid units, and a slant side with a horizontal change of 2 grid units and a vertical change of 8 grid units (relative to the left - hand side vertices).