Gem B Unit 1 Day 4 Notes
Pythagorean Theorem and the Distance Formula
I. Review of Pythagorean Theorem
A. The well-known formula: _____________________________
B. What is it used for? ____________________________________________
_____________________________________________________________
C. To use the Pythagorean Theorem correctly, you must always identify which
side “c” is.
1. __________________________________________
2. __________________________________________
3. The “____________________________”
D. Examples: (answers are given after the last example)
1. Find c.
2. Find a.
c
3
10
a
14
6
c = ___________
3. Find x.
a = ________
4. Find y.
x
5
y
15
3
9
x = ______
y = ________
Answers:
3 5,
4 6,
6 2,
5 10
II. Where does the distance formula come from?
A. Recall that we said that if a segment extends diagonally across a coordinate
grid, that counting blocks will not tell us the length of the segment.
1.
2.
B(3, 0)
B(6, 4)
A(1, 2)
C
A(-2, -5)
C
How long is AC? ________
How long is BC ? _______
Find mAB. _______
Find mAB. _______
III. The Distance Formula: _______________________________________________
A. It is a form of the Pythagorean Theorem that accepts coordinates, rather than
lengths of sides of triangles.
B. Example with diagram.
B(10, 10)
Find the measure of AB by using the
distance formula.
A(1, 2)
C. Is the segment connecting points A(-2, 5) and B(4, 2) longer, shorter or equal to the
line connecting point A with point C(2, 9) ?
Show your work and explain how you answered the question.
HW: Handout