Chapter 2: Review

Basic Formulas

Distance Formula:                

Midpoint Formula:                

Slope Of A Line:                   

Equation Of A Line

Vertical Line:                        

Horizontal Line:                    

Point-Slope Form:                 

General Form:                        .

Slope-intercept form:   (m is the slope and b is the y-intercept).

Parallel Lines:

Two lines are parallel if and only if they have the same slope.

Perpendicular Lines:

Two lines are perpendicular if and only if the product of their slopes is –1.

Equation Of A Circle

Standard Form:                     

(a,b) is the center and r is the radius.

Expanded Form:                    

Review Exercises

R2.1    Find an equation for the line given the information:

(i)                  The line passes through the points (-1,5) and (2,-3).

(ii)                The line passes through the point (0,5) and has a slope of 3.

(iii)               The line passes through the point (1,1) and is parallel to .

(iv)              The line passes through the point (-2,1) and is perpendicular to

R2.2    Verify that the points (3,4), (1,1), and (-2,3) are the vertices of an isosceles triangle.

R2.3    Explain why the triangle whose vertices are (-2,0), (-4,4), and (8,5) is a right triangle.

R2.4    Three points are said to be collinear if they lie on the same line. Show that the points (2,5), (6,1), and (4,3) are collinear.

R2.5    Find the center and the radius of each circle:

(i)                 

(ii)               

(iii)              

(iv)             

R2.6    The points (1,1), (4,15), and (7,9) lie on a circle centered at (4,5).

(i)                  Find the radius of such a circle.

(ii)                Write an equation for such a circle.