91Ó°ÊÓ

Use the distance formula to find the distance between the two points.

Does the slope of the line appear to be positive, negative, zero, or not defined?

Find the slope of the line through the points named. If the slope is not defined, write not defined.

(0, 0); (5, 1)

In Exercises 4-9 state:

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

In Exercises 4-9 state:

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

a. Find the slope of AB.

b. Find tan n°.

c. Consider the statement: If a line with positive slope makes an acute angle of n° with the x-axis, then the slope of the line is tan n°. Do you think this statement is true or false? Explain.

Find the slope of the line through the points named. If the slope is not defined, write not defined.

(7, 2); (2, 7)

Use the distance formula to find the distance between the two points.

(-8, 6) and (0, 0)

This exercise provides a geometric method of justifying the fact that you can use any two points on a line to determine the slope of the line. Horizontal and vertical segments have been drawn as shown. Supply the reason for each step.

Key steps of proof:

$\begin{array}{l}1.\text{ }∠Bâ‰\dots ∠A\\ 2.\text{ }∠1â‰\dots ∠2\\ 3.\text{ }\mathrm{Δ}LBN~\mathrm{Δ}DAJ\\ 4.\text{ }\frac{BN}{AJ}=\frac{LB}{DA},\text{ }or\text{ }\frac{BN}{LB}=\frac{AJ}{DA}\end{array}$

5. The slope of LN equals$\frac{BN}{LB}$ and the slope of DJ equals$\frac{AJ}{DA}$

6. Slope of LN equals to slope of DJ.

In Exercises 4-9 state:

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.