1. 1-1b: The Coordinate Plane - Distance Formula & Pythagorean Theorem
CCSS
G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
GSE:
M(G&M)–10–9 Solves problems on and off the coordinate plane
involving distance, midpoint, perpendicular and parallel lines, or slope
M(G&M)–10–2 Makes and defends conjectures, constructs geometric
arguments, uses geometric properties, or across disciplines or contexts
(e.g., Pythagorean Theorem

2. Example: Find the measure of AB.
Point A is at 1.5 and B is at 5.
So, AB = = 3.5

3. Example Find the measure of PR Ans: |3-(-4)|=|3+4|=7
Would it matter if I asked for the distance from R to P ?

4. Ways to find the length of a segment on the coordinate plane
1) Pythagorean Theorem- Can be used on and off the coordinate plane
2) Distance Formula – only used on the coordinate plane

5. 1) Pythagorean Theorem*
* Only can be used with Right Triangles
What are the parts to a RIGHT Triangle?
Right angle
2 legs
Hypotenuse
Hypotenuse- Side across from the right angle. Always the longest side of a right triangle.
LEG
Right angle
Leg – Sides attached to the Right angle

6. Pythagorean Formula

7. Example of Pyth. Th. on the Coordinate Plane
Make a right Triangle out of the segment
(either way)
Find the length of each leg of the right Triangle.
Then use the Pythagorean Theorem to find the
Original segment JT (the hypotenuse).

8. 8 Find the length of CD using the Pythagorean Theorem
We got 10 by | | 10 8
We got 8 by | -4 – 4|

9. Ex. Pythagorean Theorem off the Coordinate Plane
Find the missing segment- Identify the parts of the triangle
Leg
5 in
Leg 2 + Leg 2 = Hyp 2
Ans: X 2 = 13 2
Leg
13 in
25 + X 2 = 169
hyp
X 2 = 144
X = 12 in

10. 2) Distance Formula
Lets Use the Pythagorean Theorem

11. d =
J (-3,5) T (4,2)
x1, y x2, y2
Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values
(4-(-3))2 + (2-(5))2
(4+3)2 + (2-5)2
(7)2 +(-3)2 58
49+9 ~ =
7.6 ~

12. Example of the Distance Formula
Find the length of
the green segment
Ans: or approximately 10.44

13. Segments that have the same length. If AB & XY have the same length,
( ) Congruent Segments
Segments that have the same length.
If AB & XY have the same length,
Then AB=XY,
but
AB XY
Symbol for congruent

14. Assignment