The Plane

1. The Distance Formula

Recall that for two points (a,b) and (c,d) in a plane that the distance is found by the formula

Example 1

Find the distance between the points

(1,1) and (-4,3)

Solution

2. The Midpoint Formula

For points (a,b) and (c,d) the midpoint of the line segment formed by these points has coordinates:

 Midpoint Formula

Example:

Suppose that you have a boat at one side of the lake with coordinates (3,4) and your friend has a boat at the other side of the lake with coordinates (18,22).  If you want to meet half way, at what coordinates should you meet?

Solution:

M = ((3 + 18)/2,(4 + 22)/2) = (10.5,13)

Exercises

1. Show that the points (-5,14), (1,4), and (11,10) are vertices of an isosceles triangle.

2. Show that the triangle with vertices (1,1), (-1,-1), and (sqrt(3),-sqrt(3)) are vertices of a right triangle.

3. Graphing on a Calculator

We will graph the equations:

1. y = 2x - 3  (Use graph then y(x) =)

2. y = 5x2 + 4

3. y = |x + 1|  (To find absolute value, use catalog then hit enter)

4. y = 2x + {-1,0,1,2,3,5} (find the curly braces "{" and "}" use the list feature)

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