Showing posts with label Midpoint. Show all posts
Showing posts with label Midpoint. Show all posts

Wednesday, June 26, 2013

Distance and Midpoint Formulas

In this section we will review the distance and midpoint formulas.
Notice that the distance formula results in a real number and that the midpoint formula results in an ordered pair.

[ Interactive: Distance and Midpoint ]

Given two points find the distance and midpoint between them.
   

   
   
   
Video Lessons:
 
Use the distance and/or midpoint formulas to solve the following.

Example: If the diameter of a circle is defined by the two points (-3, 4) and (7, 4), find the center and radius of the circle. (Hint: diameter = 2r)
Example: Find the area of a circle given center (-3, 3) and point (3, 3) on the circle.
   
Video Examples on YouTube:





 
YouTube Example: Find the coordinates of an endpoint given the other endpoint and the midpoint.
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Monday, April 22, 2013

Interactive: Distance and Midpoint

Interactive Instructions: Move the green points A and B. Hover over the points to see the coordinates. You can also drag the line segment.




Friday, November 2, 2012

Rectangular Coordinate System

Sometimes referred to as the rectangular coordinate system, the Cartesian coordinate system consists of two perpendicular real number lines intersecting at zero. Positions on this grid system are identified using ordered pairs, (xy). The center of the system (0, 0) is called the origin.  The x-coordinate indicates horizontal distance from the origin and the y-coordinate indicates vertical distance from the origin.


The horizontal number line, usually called the x-axis, is typically used for the independent variable. The vertical real number line, usually called the y-axis, is used for the dependent variable.
Ordered pairs with 0 as a coordinate do not lie in a quadrant; these points lie on an axis.

Example: Find the distance and midpoint between the two points: (3, 4) and (−1, 2).
  
Example: Find the distance and midpoint between the two points: (0, 0) and (−3, 4).
               
Example: Find the distance and midpoint between the two points: (−1,−1) and (1,1).
       
Example: Find the distance and midpoint between the two points: (−2,−5) and (−4,−3).
             
Circle Word Problem: If the diameter of a circle is defined by two points (−3, 4) and (7, 4), find the center and radius of the circle.  (Hint: diameter = 2*radius)
       
Area of a Circle: Find the area of a circle given the center (−3, 3) and a point (3, 3) on the circle.
         
Video Examples on YouTube: