# Distance, Midpoint &amp, Circles in the Coordinate Plane

Graphs and Equations
Start by making statements such as the fol lowing : Graphs provide a means of displaying, in-
terpreting, and analyzing data in a visual format. Many real -world situations can be described
mathematically using equations in two variables . Each pair of variables re presents a solution to
the equation
and can be displayed as a single point, or ordered pair (x, y), on a coordinate plane.
The coordinate plane is devised of two perpendicular lines called the which divide
the plane into four regions, called . The horizontal line is called the
and the vertical line is called the .

Plot points : At this point, I would ask students how to describe how to plot a point or two, which
quadrant the point lies in, etc.

Solutions of Equations: How many different ways can you show, or prove, that a pair is a
solution? The relationship among ordered pairs, solutions to equations, and points on a graph is
essential.

De termine whether each ordered pair is a solution of 2x + 3y = 18.
(a) (-5, 7)
(b) (3, 4)
(c) If (4,A) is on the graph of 2x - 5y = 8, find A. This is a typical homework/test question.

Graphs of Equations:
To graph an equation is to make a drawing that represents the of that equation.
Students should be able to graph by plotting points, key points are the intercepts.

An x-intercept is a point (a, 0). To nd a, .
The x-intercept is also called a zero because

A y-intercept is a point (0, b). to nd b, .

Examples: Graph by nding intercepts.
2x + 3y = 18
3x - 5y = -10

Graph y = x2-9x-12 by plotting points. [Create a table of points by using a graphing calculator.]

Distance This is one of the last topics in Math 002 and should be familiar to students.
The distance d(P1, P2) between two points P1(x1, y1) and P2(x2, y2) is given by

Use the distance formula to verify that (-6, 3), (3,-5), and (-1, 5) form a right triangle. .. or
some other example where the students need to show they know how to use the distance formula.

Find all points having an x-coordinate of 4 whose distance from (-3,-1) is 13. This can be done
by the distance formula and/or by plotting points and reasoning through the Pythagorean Theorem.
Start by making a sketch, then ask for suggestions.

Midpoint Midpoint is pretty intuitive, although students may later confuse the formula with the
formula for slope.

The coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by

Example: Find the midpoint of the hypotenuse in the right triangle above. Extra. Use if time and
if the above example was used.

Circles Circles will be new to Math 002 students. Many have not had a geometry course for several
years. Connect to the distance formula.

De nition: A circle is the set of all points that are from a given point. The
given point is . The constant distance is called the .

The general form for the equation of a circle is:

The standard form for the equation of a circle is: where
is the and is the .

1. Identify the center and radius for the circle given by (x - 1)2 + (y - 5)2 = 4.

2. Write the equation for the circle with center at and radius . Sketch the graph.
Do variations of this question with center on an axis, in di erent quadrants, etc. and radii
that are integers as well as simple radicals , like and so on.

3. Find the center and radius of the circle given by x2 + y2 - 6x - 4y - 4 = 0. completing the
square is a familiar , but not necessarily pro cient, skill for Math 002 students.

4. What is the center of the circle with diameter endpoints at (-2, 5) and (4,-3)? Write the
equation of this circle.

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

 Algebra Helper Download (and optional CD) Only \$39.99 Click to Buy Now: OR
2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of May 23rd you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

 Algebra Helper Download (and optional CD) Only \$39.99 Click to Buy Now: OR
2Checkout.com is an authorized reseller
of goods provided by Sofmath

 "It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..." C. Sievert, KY

 Sofmath 19179 Blanco #105-234San Antonio, TX 78258 Phone: (512) 788-5675Fax: (512) 519-1805
 Home   : :   Features   : :   Demo   : :   FAQ   : :   Order Copyright © 2004-2018, Algebra-Answer.Com.  All rights reserved.