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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Solving Systems of Linear Equations by Elimination

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Exercise 4 Page 216

To obtain the image of a vertex after a dilation with scale factor k, multiply its coordinates by k.

Graph:

Type of Dilation: Enlargement.

Practice makes perfect

A dilation can be an enlargement, a reduction, or the same size as the preimage. Which type of dilation it is depends on the value of the scale factor k.

Enlargement	k>1
Reduction	0
Same	k=1

When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image.

ccc Preimage & & Image [0.5em] (x,y)& ⇒ & ( kx, ky) Since the value of k is larger than 1, we will have an enlargement of the preimage. Now, let's find the coordinates of the vertices of ABC after a dilation with a scale factor k= 2.

Dilation With Scale Factor k=2
Preimage	Multiply by k	Image
A(-1,1)	( 2(-1), 2(1))	A'(-2,2)
B(1,3)	( 2(1), 2(3))	B'(2,6)
C(3,1)	( 2(3), 2(1))	C'(6,2)

We can now plot the obtained points and connect them with segments to draw the image.

dilation

Subchapter links

Try It p.212-214

Self-Assessment for Concepts & Skills p.214

Self-Assessment for Problem Solving p.215

Review & Refresh p.216

Concepts, Skills, & Problem Solving p.216-218