The Distance & Midpoint Formulas

Finding the Distance Between Two Points

Finding the Length of a Line Segment Formula given to find the distance between any two points :

Ex.1 Points: P(0,3) Q(6,5) 2 1 Find the length of line segment P and Q: 3 4

Find the distance between the points (3,5) and (6,4).

Finding the Midpoint of a Line Segment When finding the MIDPOINT of a line segment having endpoints and Find the Midpoint: Midpoint

Determine the Coordinates of the Midpoint of the line segment with endpoints:

Graphing Equations w/ TWO Variables

NAME THE COORDINATES & QUADRANT FOR EACH POINT A: (6, 5) I B: (4, 6) I C: (2, 1) I D: (-4, 3) II E: (-5, 0) x-axis F: (-3, -2) III G: (0, -4) y-axis H: (4, -4) IV

y = -3x + 6 Y X 6

y = -3x + 6 Y X 6 -1 9

y = -3x + 6 Y X 6 -1 9 1 3

y = -3x + 6 Y X 6 -1 9 1 3 2

Now DRAW the Line Y (1,3) (-1,9) X (2,0) (0,6)

Intercepts If you replace the “x” value with zero and solve for “y” you will find the y-intercept. If you replace the “y” value with zero and solve for “x” you will find the x-intercept.

Intercepts Y X y-Intercept x-Intercept

Graph. y = 3 Line is Horizontal x y y -2 3 -1 3 3 1 3 2 3 x 3 3 4 3 Any line in the form y = k will be horizontal. 5 3

Graph. x = -2 Line is Vertical x y y -2 -2 -2 -1 -2 -2 1 -2 2 x -2 3 -2 4 -2 5

Review Horizontal Lines Vertical Lines y = “a number” x = “a number”

Graph x = -4 on a coordinate plane. y x