Lesson 17: Practice Problems

Problem 1

Select all the points that are on the line through $(0, 5)$ and $(2, 8)$ .

$(4, 11)$
$(5, 10)$
$(6, 14)$
$(30, 50)$
$(40, 60)$

Problem 2

Here is triangle $A B C$ .
- Draw the dilation of triangle $A B C$ with center $(2, 0)$ and scale factor 2.
- Draw the dilation of triangle $A B C$ with center $(2, 0)$ and scale factor 3.
- Draw the dilation of triangle $A B C$ with center $(2, 0)$ and scale factor $\frac{1}{2}$ .
What are the coordinates of the image of point $C$ when triangle $A B C$ is dilated with center $(2, 0)$ and scale factor $s$ ?
Write an equation for the line containing all possible images of point $C$ .

Problem 3

All three points displayed are on the line. Find an equation relating $x$ and $y$ .

A line with points (3,3), (x,y), and (6,9).

Problem 4 From Unit 2 Lesson 7

These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle? Explain or show how you know.

Small triangle has a height of 3. Large triangle has a height of 6.

Problem 5

Here are some line segments.

Dilation point A with lines of increasing length: FH, BC, GJ, ED

Which segment is a dilation of $\overset{―}{B C}$ using $A$ as the center of dilation and a scale factor of $\frac{2}{3}$ ?
Which segment is a dilation of $\overset{―}{B C}$ using $A$ as the center of dilation and a scale factor of $\frac{3}{2}$ ?
Which segment is not a dilation of $\overset{―}{B C}$ , and how do you know?