Question

investigate reductions and enlargements

1. use tools in the space provided, sketch an enlargement that has sides $\frac{3}{2}$ the length of each given figure.

Explanation:

Step1: Understand the scale - factor

The scale - factor for the enlargement is $\frac{3}{2}=1.5$. This means each side of the new figure will be 1.5 times the length of the corresponding side of the original figure.

Step2: Sketch the enlarged figures

For the triangle: Measure each side of the original triangle. Multiply each side - length by 1.5 to get the side - lengths of the enlarged triangle. Then, using a ruler and a protractor (if needed to maintain the angles), draw the enlarged triangle.
For the trapezoid: Measure each of the four sides of the original trapezoid. Multiply each side - length by 1.5. Then, draw the new trapezoid with the calculated side - lengths, keeping the angles the same as in the original trapezoid.
For the rhombus: Measure the side - length of the original rhombus (since all sides of a rhombus are equal). Multiply this side - length by 1.5. Then, draw the new rhombus with the new side - length, maintaining the angles of the original rhombus.

Since this is a sketching problem, no single numerical answer can be provided. The task is to create the enlarged figures as described above.

Answer:

Step1: Understand the scale - factor

The scale - factor for the enlargement is $\frac{3}{2}=1.5$. This means each side of the new figure will be 1.5 times the length of the corresponding side of the original figure.

Step2: Sketch the enlarged figures

For the triangle: Measure each side of the original triangle. Multiply each side - length by 1.5 to get the side - lengths of the enlarged triangle. Then, using a ruler and a protractor (if needed to maintain the angles), draw the enlarged triangle.
For the trapezoid: Measure each of the four sides of the original trapezoid. Multiply each side - length by 1.5. Then, draw the new trapezoid with the calculated side - lengths, keeping the angles the same as in the original trapezoid.
For the rhombus: Measure the side - length of the original rhombus (since all sides of a rhombus are equal). Multiply this side - length by 1.5. Then, draw the new rhombus with the new side - length, maintaining the angles of the original rhombus.

Since this is a sketching problem, no single numerical answer can be provided. The task is to create the enlarged figures as described above.