Question

draw a scaled copy of polygon a using a scale factor of 2.

Explanation:

Step1: Identify the sides of Polygon A

Let's assume Polygon A (a right triangle) has legs of length \( l_1 \) and \( l_2 \), and hypotenuse \( h \). From the diagram, we can visually estimate or measure (if we had coordinates) the lengths. But for scaling, we use the scale factor.

Step2: Apply the scale factor

To create a scaled copy with scale factor 2, we multiply the length of each side of Polygon A by 2. So the new legs will be \( 2l_1 \) and \( 2l_2 \), and the new hypotenuse will be \( 2h \).

Step3: Draw the new triangle

Using the new side lengths, draw a right triangle (since the original is a right triangle) with legs \( 2l_1 \) and \( 2l_2 \). The angles will remain the same as the original triangle because scaling is a similarity transformation (preserves angles).

For example, if the original triangle has a vertical leg of length 3 units and a horizontal leg of length 4 units, the scaled copy will have a vertical leg of \( 3\times2 = 6 \) units and a horizontal leg of \( 4\times2=8 \) units. The hypotenuse of the original (by Pythagoras \( \sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25} = 5 \)) will be \( 5\times2 = 10 \) units in the scaled copy.

Answer:

To draw the scaled copy:

1. Measure (or determine) the lengths of the two legs (and hypotenuse) of the original right - triangle (Polygon A).
2. Multiply each of these lengths by 2.
3. Using the new lengths, draw a right - triangle. The new triangle will have the same shape (same angles) as Polygon A but each side will be twice as long. If we consider the original triangle with vertical leg length \( a \), horizontal leg length \( b \), and hypotenuse \( c=\sqrt{a^{2}+b^{2}} \), the scaled triangle will have vertical leg \( 2a \), horizontal leg \( 2b \), and hypotenuse \( 2c \). The final scaled triangle is a right - triangle similar to Polygon A with all sides doubled in length.