1.  A(0, 4)  B(-3, 0)  C(3, 5)  D(-8, -11)  E(7, -5)  F(-3.5, 7.5)

3. Essential Question: How do you calculate distance, midpoint, and slope on a coordinate plane?

4.  Origin  x-axis  y-axis  Quadrants  Coordinates  Positive  Negative

6.  Why?

7.  What is the midpoint of 7 and 15?  What is the midpoint of (2, 7) and (4, 1)?

11.  Mary walks 3 miles north and 2 miles east. Her boyfriend John walks 2 miles south and 4 miles west. What is the straight line distance from their hearts?

14. Essential Question: How do the slopes of parallel and perpendicular lines relate?

15.  Line with slope, m = -2, through (3, -5)

16.  y = mx + b  m =  b =

18.  b(egin) =  m(ove)=

19.  Point-Slope  Slope Intercept

21.  x-int (set y=0)  y-int (set x=0)

22.  Solve for y:  b(egin)  m(ove)

23.  b(egin) =  m(ove)=

24.  (10, 2) & (2, -2)  Step 1: Find Slope  Step 2: Combine pt & slope

25.  Slope:  Equation:

26.  What is special?  Horizontal:  Vertical:

30. Essential Question: How do the slopes of parallel and perpendicular lines relate?

31.  Are these parallel?

32.  Can you write the equation of a 3 rd line that is parallel?

34.  They are OPPOSITE RECIPROCAL slopes.

36.  Step 1: Perpendicular Slope:  Step 2: Combine Point & Slope:

37.  Write the equation of the Line through (3, 2), which is perpendicular to 3x + 2y = -6.

39. Essential Question: How can slope, distance and/or midpoint be used to establish properties of a plane figure?

40. How should we draw it? › Origin & x-axis.

45. Essential Question: How can slope, distance and/or midpoint be used to establish properties of a plane figure?

46.  Can we PROVE that the midpoints of a Rhombus form a Rectangle?  Conveniently Plot a Rhombus, then find its midpoints…

48.  Midsegment is Parallel to Base and ½ the length of the 3 rd side!  Place Triangle. Find Midpoints, calculate slope and length of Midsegment.

49.  Plan out a Proof: