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2 years ago

Devin said that AB and CD for A(-2, 0), B(2, 3), C(1, -1), and D(5, --4) are parallel. Explain and correct Devin's error.

Mathematics

1 answer:

defon2 years ago

7 0

Answer:

See below

Step-by-step explanation:

Slope of AB is correct

Slope of CD is incorrect

Slope of AB = (3 - 0)/(2 - (-2)) = 3/4
Slope of CD = (-4 - (-1))/(5 - 1) = -3/4

Slopes are different, lines are not parallel

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Answer:

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Step-by-step explanation:

The complete and correct question is

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.

Which of the following statements are true about the lengths of the trails? Check all that apply.

1.The total length of the Dogwood Trail is 16 kilometers.

2.The total length of the Dogwood Trail is 24 kilometers.

3.The Elm Trail is longer than the Dogwood Trail.

4.The difference between the lengths of the trails is 2 kilometers.

5.The difference between the lengths of the trails is 6 kilometers.

The picture in the attached figure

step 1

Find the value of a

Applying the Pythagorean Theorem in the right triangle ABC

$13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km$

step 2

Find the value of b

Applying the Pythagorean Theorem in the right triangle CDE

$5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km$

step 3

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substitute the given values

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Verify the following statements

Part 1) The total length of the Dogwood Trail is 16 kilometers

The statement is false

Because

The total length of the Dogwood Trail is 24 kilometers (see the explanation)

Part 2) The total length of the Dogwood Trail is 24 kilometers

The statement is true (see the explanation)

Part 3) The Elm Trail is longer than the Dogwood Trail

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Because

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Part 4) The difference between the lengths of the trails is 2 kilometers

The statement is false

Because

The difference is equal to

$24-18=6\ km$

Part 5) The difference between the lengths of the trails is 6 kilometers

The statement is true

Because

The difference is equal to

$24-18=6\ km$

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