1. Warm-up
Use the Pythagorean theorem to find the missing length of the right triangle. Round to the nearest tenth.
Determine whether the given lengths are sides of a right triangle.
3. 8, 15, , 6, , 40, 41 c 2 17 8 5 b

2. How do I find the distance between two points without a ruler?
Acc. Alg./Geom. A Day 52 ( )
UNIT QUESTION: How do we use algebraic methods with geometry to solve problems involving location and distance?
Standard: MM1G1
Today’s Question:
How do I find the distance between two points without a ruler?
Standard: MM1G1.a.

3. Unit 6 The Distance Formula
(x2,,y2) d
(x1,,y1)
(x2,,y1)

4. Unit 6 The Distance Formula
(3,4)
(1,1)

5. Unit 6 The Distance Formula

6. Steps to solving the Distance Formula
Write the distance formula
Plug in the coordinates of 2 points
Remember PEMDAS!

7. Let's Practice!! Example #1
Use the distance formula to find the distance
between (1, 4) and (-2, 3)

8. Example #2
Use the distance formula to find the distance between the points, (10, 5) and (40, 45).
D = 50

9. 3. Find the distance between the points.

10. 5. Find the distance between the points.

11. 6. The distance d between two points is given
6. The distance d between two points is given. Find the possible values of b.

12. Put it all together!
On a road trip, you hike 3 miles north and 2miles west. Starting at the same point, your friend hikes 4 miles east and 1 mile south.
How far apart are you?
If you want to meet for lunch, where could you meet so each person goes the same distance?

13. The Midpoint Formula

14. The midpoint between (x1, y1) and (x2, y2) is
The Midpoint Formula
The midpoint of a line segment is the point on the segment that is equidistant from its endpoints
The midpoint between (x1, y1) and (x2, y2) is

15. Example
Find the midpoint of the line segment connecting the given points. (-2, 3) and (4, 2)

16. Example
Find the midpoint of the line segment connecting the given points. (200, 75) and (25, 175).

17. Example
Point A is at (3, 1). The midpoint is at (6, -1). Find the other point on the line segment AB.

18. Example
Find the midpoint of the line segments.

19. Perimeter and Area of Shapes
Use distance formula to solve the perimeter and area of the shape.