**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 and

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

Then we can rearrange the equation to solve for d

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 and , then:

the average of the x values would be ,

and the average of the y values would be ,

so to find the coordinates of M we can use this 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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