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D1

Page history last edited by PBworks 17 years, 1 month ago
 Outcome: D1 - develop and apply formulas for distance and midpoint

 

Originator: Kristen and Ian

 

Explanation: To find the distance (d) between two points on a coordinate graph, we can draw a line between the two points, and then draw a triangle with this line as the hypotenuse.  Using algebra, we can determine that the two legs of the triangle have lengths Formula and Formula

 

 

Now we can use the Pythagorean Theorem to determine the length of the hypotenuse.

Formula

Formula

Then we can rearrange the equation to solve for d

Formula

 

This is the formula for finding the distance between two points.

 

 

To find the midpoint (M) of two points, we need to find the x value that is halfway between the x values of the two points, and the y value that is halfway between the y values of the two points.  This will give us the coordinates of the midpoint.  To find these halfway values, we can find the average of the two x values and the average of the two y values. 

For example, if the two points were Formula and Formula, then:

the average of the x values would be Formula,

 

and the average of the y values would be Formula,

 

so to find the coordinates of M we can use this formula:

 

 

Formula 

 

Problem:

Bob and Tim are on a jungle gym. Bob is at point (1,3) and Tim is at point (3,1)

a) how far far would bob have to go to get to tim if he traveled a straight line?

b) if they both traveled an equal distant, at what point would they meet up?

 

 

Solution

a) d^2=(3-1)^2 + (1-3)^2 = 2^2 + (-2)^2= 4 +4 = 8

    d= square root of 8, which is equal to 2.8units

b) midpoint = (((1+3)/2), ((3+1)/2))) = (4/2, 4/2) = (2,2) therefore they would meet at point (2,2)

 

Comments (1)

Anonymous said

at 7:11 pm on Jun 14, 2007

Very nicely done Kristen and Ian.

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