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3.09 Slopes of lines and similar triangles

Worksheet
Slopes of lines
1

Consider the straight line that passes through the points A, \, B, C and D:

a

Find the slope of the line using the points A and D.

b

Find the slope of the line using the points B and C.

-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
10
12
14
y
2

Consider the points A, \, B, and C on the following coordinate plane:

a

Describe how to move from point A to the following points:

i

Point B

ii

Point C

b

Express the direction of the following movements as a simplified ratio, comparing vertical movement to horizontal movement:

i

From point A to point B

ii

From point A to point C

-1
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
8
9
10
11
12
13
y
3

Consider the points A, \, B, and C on the following coordinate plane:

a

Describe how to move from point A to the following points:

i

Point B

ii

Point C

b

Express the direction of the following movements as a simplified ratio, comparing vertical movement to horizontal movement:

i

From point A to point B

ii

From point A to point C

-2
2
4
6
8
10
12
14
16
x
-2
2
4
6
8
10
12
14
16
y
4

Consider the points A, \, B, and C on the following coordinate plane:

a

Describe how to move from point A to the following points:

i

Point B

ii

Point C

b

Express the direction of the following movements as a simplified ratio, comparing vertical movement to horizontal movement:

i

From point A to point B

ii

From point A to point C

c

Does the slope of the interval between A and B is equal to the slope between the points B and C?

-2
2
4
6
8
10
12
x
-2
2
4
6
8
10
12
14
16
y
5

Consider the points A, \, B, and C on the following coordinate plane:

a

Describe how to move from point A to the following points:

i

Point B

ii

Point C

b

Express the direction of the following movements as a simplified ratio, comparing vertical movement to horizontal movement:

i

From point A to point B

ii

From point A to point C

iii

From point B to point C

c

Determine the slope of the line.

-15
-10
-5
5
10
x
-8
-7
-6
-5
-4
-3
-2
-1
1
2
y
6

Consider the points A, \, B, and C on the following coordinate plane:

a

Describe how to move from point A to the following points:

i

Point B

ii

Point C

b

Express the direction of the following movements as a simplified ratio, comparing vertical movement to horizontal movement:

i

From point A to point B

ii

From point A to point C

c

Determine the slope of the line.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-8
-6
-4
-2
2
4
6
8
10
y
7

Consider the points A, \, B, and C on the following coordinate plane:

a

Describe how to move from point A to the following points:

i

Point B

ii

Point C

b

Express the direction of the following movements as a simplified ratio, comparing vertical movement to horizontal movement:

i

From point A to point B

ii

From point A to point C

c

Determine the slope of the line.

-6
-4
-2
2
4
6
8
10
12
14
x
-4
-2
2
4
6
8
10
y
8

Consider the points A and B on the straight line:

a

Describe how to move from point A to point B.

b

Express the direction of the movement in part (a) as a simplified ratio, comparing vertical movement to horizontal movement.

c

Now, find y if the coordinates of C are \left(2, y \right) and C also lies on the same line.

-4
-3
-2
-1
1
2
3
4
x
-8
-6
-4
-2
2
4
6
8
y
9

Consider the points A and B on the straight line:

a

Describe how to move from point A to point B.

b

Express the direction of the movement in part (a) as a simplified ratio, comparing vertical movement to horizontal movement.

c

Now, find x if the coordinates of C are \left(x, - 19 \right) and C also lies on the same line.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-3
-2
-1
1
2
3
4
5
6
7
y
Similar triangles
10

\triangle ABD is similar to \triangle ACE, with points A \left(2, 4\right), B \left(4, 10\right) and C lying on a straight line:

a

Determine the slope of the straight line.

b

If length EC is 18 units, determine the coordinates of point C.

x
y
11

\triangle BCD is similar to \triangle BAE, and points A \left(3, - 5 \right), B, and C lie on a straight line with slope - 4:

a

If length BE is 7 units, determine the coordinates of point B.

b

If length BD is 48 units, determine the coordinates of point C.

x
y
12

Consider the following coordinate plane:

Determine whether the following triangles are similar to \triangle ABC:

a

\triangle ECD

b

\triangle AED

c

\triangle ABF

d

\triangle EFD

-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
y
13

Consider the following coordinate plane:

Determine whether the following triangles are similar to \triangle ABC:

a

\triangle ABF

b

\triangle FCD

c

\triangle ECD

d

\triangle EFD

-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
y
14

Consider the following coordinate plane:

Determine whether the following triangles are similar to \triangle FDB:

a

\triangle AFB

b

\triangle BAE

c

\triangle CFB

d

\triangle EDC

-7
-6
-5
-4
-3
-2
-1
1
2
3
4
x
-14
-12
-10
-8
-6
-4
-2
2
4
y
15

Consider the following coordinate plane:

Determine whether the following triangles are similar to \triangle FDB:

a

\triangle EFA

b

\triangle CBA

c

\triangle AEB

d

\triangle CFB

-8
-6
-4
-2
2
4
6
x
-12
-10
-8
-6
-4
-2
2
4
6
8
10
y
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Outcomes

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Given a table, graph or written description of a linear relationship, determine the slope.

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Solve mathematical and real-world problems involving proportional relationships between similar triangles.

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