Question

relating areas of scale drawings 1. create a scale drawing of the triangle by using the scale factor of 3.

Explanation:

Step1: Identify original triangle dimensions

Assume the original triangle (right - angled) has a vertical leg of length \(h = 2\) units and a horizontal leg of length \(b=4\) units (from the grid).

Step2: Apply scale factor to dimensions

The scale factor is \(k = 3\). For a scale drawing, the new length of the vertical leg \(h_{new}=k\times h\) and the new length of the horizontal leg \(b_{new}=k\times b\).
So, \(h_{new}=3\times2 = 6\) units and \(b_{new}=3\times4=12\) units.

Step3: Draw the scaled triangle

On the grid, draw a right - angled triangle with one leg (vertical) of length 6 grid units and the other leg (horizontal) of length 12 grid units. The right angle is between these two legs, and the hypotenuse will be formed by connecting the endpoints of these two legs.

Answer:

To create the scale drawing:

1. Determine the original triangle's leg lengths (e.g., vertical leg = 2 units, horizontal leg = 4 units from the grid).
2. Multiply each leg length by the scale factor of 3: vertical leg becomes \(2\times3 = 6\) units, horizontal leg becomes \(4\times3=12\) units.
3. Draw a right - angled triangle on the grid with vertical leg of 6 units, horizontal leg of 12 units, and a hypotenuse connecting their endpoints.