Real Numbers And The Pythagorean Theorem Worksheet - Chapter 7 Page 33
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463 3
ACTIVITY:
Developing the Distance Formula
Work with a partner. Follow the steps below to write a formula
that you can use to fi nd the distance between any two points in
a coordinate plane.
y
5
4
3
2
1
5
4
3
2
1
1
2
3
4
5
x
2
3
4
5
Step 1: Choose two points in the coordinate plane that do not lie on the same
horizontal or vertical line. Label the points (x
, y
) and (x
, y
).
1
1
2
2
Math
Step 2: Draw a line segment connecting the points. This will be the
Practice
hypotenuse of a right triangle.
Communicate
Step 3: Draw horizontal and vertical line segments from the points to
Precisely
form the legs of the right triangle.
What steps can you
Step 4: Use the x-coordinates to write an expression for the length of the
take to make sure
horizontal leg.
that you have
written the distance
Step 5: Use the y-coordinates to write an expression for the length of the
formula accurately?
vertical leg.
Step 6: Substitute the expressions for the lengths of the legs into the
Pythagorean Theorem.
Step 7: Solve the equation in Step 6 for the hypotenuse c.
What does the length of the hypotenuse tell you about the two points?
IN YOUR OWN WORDS
4.
In what other ways can you use the Pythagorean
Theorem?
5. What kind of real-life problems do you think the converse of the
Pythagorean Theorem can help you solve?
Use what you learned about the converse of a true statement to
complete Exercises 3 and 4 on page 322.
Section 7.5
Using the Pythagorean Theorem
319
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