Math 170 - CooleyPre-Calculus OCC

Section 1.3 – Equations and Graphs in Two Variables

The Cartesian/Rectangular Coordinate System

Pythagorean Theorem

In any right triangle, if a and b are the length of the

Lengths of the legs and c is the length of the hypotenuse,

then .

The Distance Formula

The distance d between any two points and is given by the formula

The Midpoint Formula

The midpoint of the line segment with endpoints and , is

.

Equation for a Circle in Standard Form

The equation for a circle with center (h,k) and radius rfor r > 0 is

A circle centered at the origin has equation.

Graph of the Equation of a Circle (Standard Form)

Rule for Completing the Square of x2 + bx + ?

The last term of a perfect square trinomial (with a = 1)is the square of one-half of the coefficient of the middle term. In symbols, the perfect square trinomial whose first two terms arex2 + bxis

.

Theorem – Equation of a Line in Standard Form

If A, B, and C are real numbers, then the graph of the equation

is a straight line, provided A and B are not both zero. Every straight line in the coordinate plane has an equation in the form , the standard form for the equation of a line.

 Exercises:

Plot and label each group of points on the same set

of axes below and identify which quadrant each

point is located.

1) A( 4 , 8 )

2) B( –6 , –10 )

3) C( 1 , –7 )

4) D( –3 , 0 )

 Exercises:

5)Find the distance between the pair of points: and

6)Find the midpoint of the segment with the given endpoints: and

Determine the center and the radius of each circle and sketch the graph.

7)8)

 Exercises:

9)Write the standard equation for the circle satisfying the given conditions: Center , radius 11

10)Write the standard equation for thecircle satisfying the given conditions: Center , radius

11)Write the standard equation for the circle satisfying the given conditions:

Center , passing through

Find the center and the radius of each circle. Then graph the circle.

12)

13)

 Exercises:

Sketch the graph of the linear equation. Be sure to find and show the x- and y- intercepts.

14)

Graph each equation in the rectangular coordinate system.

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