6th Grade Math Textbook, Fundamentals

Lesson 13-12 for exercise sets. &KDSWHU 

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1.Draw a triangle with vertices (1, 0), (2, 1), (2, 2). Use a coordinate grid to

create two dilations: one with a scale factor of 4 and one with a scale factor

of.

2.Discuss and Write Explain how to determine whether one figure is a

dilation of another figure.

1

4

Using the coordinates of a dilation, you can find its area.

The length of a vertical line segment with endpoints (x 1 , y 1 )

and (x 1 , y 2 ) is |y 1 y 2 |. The length of a horizontal line segment

with endpoints (x 1 , y 1 ) and (x 2 , y 1 ) is |x 1 x 2 |.

What is the area of each dilated figure on page 374?

Enlargement

Find the base.

The endpoints of the base are (9, 0)

and (9, 0).

So the base is: | 9 9| |18 |  18

Find the height.

The endpoints of the height are (0, 12)

and (0, 0).

So the height is: |12 0| |12|  12

Use the area formula.

A bh (18)(12) 108 units^2

So the area of the enlarged triangle

is 108 units^2

1

2

1

2

Reduction

Find the base.

The endpoints of the base are (1.5, 0)

and (1.5, 0).

So the base is: |1.5 1. 5 | |3|  3

Find the height.

The endpoints of the height are (0, 2)

and (0, 0).

So the height is: | 2 0| |2|  2

Use the area formula.

A bh (3)(2) 3 units^2

So the area of the reduced triangle

is 3 units^2

1

2

1

2

Rectangle WXYZhas vertices W(3, 2), X(6, 2), Y(6, 3), Z(3, 3).

Rectangle PQRShas vertices P(8, 6), Q(7, 6), R(7, 1), S(8, 1).

Is rectangle PQRSa dilation of rectangle WXYZ? If it is a dilation,

tell whether it is an enlargement or a reduction.

Compare the lengths of corresponding line segments.

Rectangle WXYZ Rectangle PQRS

WX ZY |3 6|  3 PQSR| 8 7|  15

WZXY| 2 (3)|  1 PSQR|6 1|  5

The lengths of the corresponding sides ofPQRS andWXYZ

are in a ratio of 5 : 1. SoPQRS is a dilation ofWXYZ.It is an

enlargement with a scale factor of 5.

1

Think

(^153) 5 and (^51)  5