MM Dilations and similar figures

Review of Dilations and similar figures

by Coach Miller

​Get out paper & pencil for notes & space to work out problems.

​Lesson Information

​standards: MGSE9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.

a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

​Learning targets: use the definition of dilation or the dilation coordinate rule to perform dilations on the coordinate plane.

• evaluate shapes on the coordinate plane to determine the scale factor and center of a dilation that has occurred.

• check the lengths of various sides to determine if they are proportional.

Essential Questions

​Describe what happens when you perform a dilation. 

What data was used to evaluate the scale factor of the dilation?

Multiple Choice

All angles in similar figures are congruent.  

• True
• False

Multiple Choice

Which side length corresponds with EF?

• ML
• LM
• OL
• EH

Multiple Choice

Line CB corresponds with what line? 

• SR
• PQ
• SP
• RQ

Multiple Choice

What is the formula for scale factor?

• $$\frac{new}{old}$$

• $$\frac{old}{new}$$

Multiple Choice

What is the scale factor from the small fry to the large fry?

• 1/3

• 48

• 4

• 3

Multiple Choice

What is the scale factor from the smaller quadrilateral to the larger?

• scale factor = 4
• scale factor = 10
• scale factor = 3
• scale factor = 2

Multiple Choice

What is the scale factor? from large shape to small shape. The small shape is the NEW image

• 1

• 2

• 1/2

• -2

Multiple Choice

What is the scale factor from ΔABC to ΔDEF?

• 1/2

• 7/3

• 2

• 10/3

​Determining coordinates based off scale-factor

​1st ensure that the center of dilation is the origin

2nd identify coordinates

3rd multiply each part of the coordinate by the scale factor 

​

​M (-4,6) --> (-4*1.5, 6*1.5) = M'(-6, 9)

​N (2, 6) --> (2*1.5, 6*1.5) = N'(3,9)

​If they ask you to identify the original coordinates, go backwards by dividing by the scale factor

Multiple Choice

How do you write the algebraic notation when the scale factor is 3?

• (x, y) goes to (1/3x, 1/3y)
• (x, y) goes to (-3x, -3y)
• (x, y) goes to (x + 3, y + 3)
• (x, y) goes to (3x, 3y)

Multiple Choice

Which algebraic expression could be the rule for a reduction?

• (x, y)→(2x, 2y)
• (x, y)→(5/2 x, 5/2 y)
• (x, y) →(0.5x, 0.5y)
• (x, y)→(5x, 5y)

Multiple Choice

Dilate Point B by a scale factor of 3:

• (12,0)
• (12,12)
• (4,3)
• (0,12)

Multiple Choice

The rule for the dilation of quadrilateral QRST to the image Q'R'S'T' is  D_O,0.5(x, y) → (0.5x, 0.5y).

What are the coordinates of Q', if Q(0, 2)?

• (0,1)

• (1,0)

• (0,4)

• (4,0)

Multiple Choice

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)
• (20,12)
• (-20,-12)
• (-5,-3)

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's a reduction; the scale factor is 2.
• It's an enlargement; the scale factor is 2.
• It's an enlargement; the scale factor is 1/2.
• It's a reduction; the scale factor is 1/2.

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's an enlargement; the scale factor is 1/2.
• It's an enlargement; the scale factor is 2.
• It's a reduction; the scale factor is 1/2.
• It's a reduction; the scale factor is 2.

Multiple Choice

When the scale factor of a dilation is less than one, the dilation is a reduction.

• True
• False

Multiple Choice

A triangle has vertices A(0,0), B(8,0), C(3,-2). Find the coordinates of the triangle after a dilation with a scale factor of  4. The dilation is (X,Y) --- (4x,4y)

• A(3,3), B(4,4), C(-3,-4)
• A(-4,8), B(6.5,8), C(7,7)
• A(0,0), B(32,0), C(12,-8)

Multiple Choice

Name the series of transformations that maps ABC onto DEF

• reflect over x then translate left 6 up 1
• reflect over y then translate down 6 left 1
• translate right 6 down 1, then reflect over x
• rotate 90 clockwise then reflect over y