The Plane

I.  Hand out Syllabus

II.  Introductions

III.  The Distance Formula

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

dist = sqrt[(c - a)²  + (d - b)²]

Example 1

Find the distance between the points

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

dist = sqrt[(-4 - 1)² + (3 - 1)²] = sqrt[25 + 4] = sqrt[29]

IV.  The Midpoint Formula

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

M = ((a + c)/2,(b + d)/2)

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.

V)  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)

One point of extra credit if you put the words "We Love Our Graphing Calculators" on the top of the homework that is due on Jan 7.