1. 1.6 Midpoint and Distance in the Coordinate Plane

2. Midpoint and Distance
Coordinate Plane- a plane divided into four regions by an x-axis and y-axis
Midpoint Formula:

3. Practice Problems:
Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

4. Practice Problems:
M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.
S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T.

5. Distance Formula
Distance Formula:

6. Practice Problems: Find FG and JK. Then determine whether FG  JK.

7. Practice Problems Find EF and GH. Then determine if EF  GH.

8. Right Triangles
Parts of a right triangle:
Hypotenuse
leg
leg

9. Pythagorean Theorem
For right triangles: the sum of the squares of the length of the legs is equal to the square of the length of the hypotenuse

10. Practice Problems:
Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5).
More examples: Check it out Pg. 45, #4 a) and b)