P7 The Cartesian Plane

Quick review of graphing, axes, quadrants, origin, point plotting

Distance Formula : derived from Pythagorean Theorem

2122

12 yyxxd

Examples

• Find the distance between (-2,1) and (3, 4)

• Show that (2, 1), (4, 0), and (5, 7) are vertices of a right triangle.

Midpoint Formula:

2,

22121 yyxx

Example

Find the midpoint of (-5, -3) and (9, 3)

1.1 Graphs of Equations

Sketch these two graphs

xy 37

22 xy

Intercepts of the Graph

X-intercept: where it crosses the x-axis

Y-intercept: where it crosses the y-axis

Find the x & y intercepts

3 21. 4 2. 4y x x y x

Symmetry

• x axis: (x.y) and (x, -y)

• y axis: even function (x, y) and (-x, y)

• Origin: odd function (x, y) and (-x, -y)

Testing for Symmetry

22 yx

Use intercepts and symmetry to sketch the graph.

2 1 1x y y x