Lesson 4

A rectangle with area 12 square units is dilated by a scale factor of \(k\). Find the area of the image for each given value of \(k\).

1. \(k=2\)
2. \(k=5\)
3. \(k=1\)
4. \(k=\frac14\)
5. \(k=1.2\)

The area of a circle of radius 1 is \(\pi\) units squared. Use scaling to explain why the area of a circle of radius \(r\) is \(\pi r^2\) units squared.

Trapezoid \(A’B’C’D\) was created by dilating trapezoid \(ABCD\) using \(D\) as the center of dilation.

1. What was the scale factor of the dilation?
2. Based on the scale factor, how many copies of \(ABCD\), including the original, should fit inside \(A’B’C’D\)?
3. How can you see your answer to these questions in the diagram?

Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above the plane and a scale factor between 0 and 1. Estimate the scale factor that was used for each dilation.

Dilation A

Dilation B

Dilation C

Select the solid whose cross sections are dilations of some two-dimensional shape using a point directly above the shape as a center and scale factors ranging from 0 to 1.

cone

cube

cylinder

triangular prism

Select all figures for which at least one cross section is a circle.

triangular pyramid

square pyramid

rectangular prism

cube

cone

cylinder

sphere

Triangles \(ACD\) and \(BCD\) are isosceles. Angle \(DBC\) has a measure of 110 degrees and angle \(BDA\) has a measure of 22 degrees. Find the measure of angle \(BAC\).

\(\overline{AD} \cong \overline{AC}\) and \(\overline{BD} \cong \overline{BC}\)