Math 121

Section 1.1

The Cartesian Plane and the Distance Formula

The Cartesian Plane

Quadrant I                              Quadrant II        

Quadrant III                               Quadrant IV

Independent axis is the x-axis

Dependent axis is the y-axis

Ordered pairs – (x,y)

x = x-coordinate

y = y-coordinate

Example: Graph the following ordered pairs.

(-3,1), (-2,3), (-3,-4), (4,3)

Distance formula

The distance between the points and is given by the formula:

Examples

1) Find the distance between the points (2,5) and (3,7).

2) Find the distance between the points (-3,1) and (3,-2).

Right Triangle Problems

1)      Show that the points A = (2,1), B = (4,0), and C = (5,7) form a right triangle, then find the area of the triangle.

i)                    Make a plot of the points A,B, and C

ii)                  Find the distances between the points.

iii)                Use Pythagorean Theorem to check distances

Thus, triangle ABC is a right triangle

iv)                Area of the triangle

#24 on page 8

Find x such that the distance between the point is 5 units.

(2,-1) and (x,2)