13.1 The Distance and Midpoint Formulas

Review of Graphs

Coordinate Plane

Origin

Axes: x-axis y-axis

Quadrants   VV C

The arrowhead on each side represents the positive direction

Remote Time Which quadrant does the point lie in?

Remote Time (3,1)

Remote Time (-2,-1)

Remote Time (5,-3)

Finding Distance A(3,4)B(-1,4) D(-3,-2) C(-3,1)

Horizontal Distance AB = |3-(-1)| = 4 or AB = |-1-3| = 4 A(3,4)B(-1,4)

Vertical Distance CD = |1-(-2)|= 3 or AB = |-2-1| = 3 D(-3,-2) C(-3,1)

What do I do when two points do not lie on a horizontal or vertical line……..? A(1,2) B(4,-2)

Make a right triangle A(1,2) B(4,-2) C(1,-2)

Use the pythagorean theorem A(1,2) B(4,-2) C(1,-2)

Theorem The Distance Formula: The distance d between two points is given by