Find the value of K?

Question

Find the value of K if the line joining (4,K) and (6,8) and the line joining (-1,4) and (0,8) are Parallel. Then find Perpendicular.

Please please please explain your answers.

Thanks a bunch = )

Answer 1

If two lines are parallel, then what do you know? That's right, they have the *same* slope. What is the slope of the line joining (-1,4) and (0,8)? The slope is just the "change in y" divided by the "change in x". Or, algebraically: y1-y2 / x1 - x2. So,

(4 - 8) / (-1 - 0) = -4/-1 = 4

So, now do the same for the first pair, and you *KNOW* the slope is 4.

(k - 8) / (4 - 6) = 4

(k - 8) / (-2) = 4

(k - 8) = -8

k = 0

Now, what do you know about a line perpendicular to a given line? That's right, the slope is the negative reciprocal. So, what is the negative reciprocal of 4? Yup, -1/4. So, we want a line that goes through (4, 0) (remember, K = 0), and has a slope of -1/4.

So, pick the most general point you can think of on this perpendicular line. How about the point (x,y). Is that general enough? Ok, what is the equation of a line the joins (x,y) and (4,0) and has a slope of -1/4?

I'll let you do the work, but I'll get you started:

(y - 0) / (x - 4) = -1/4

HTH

Charles

Answer 2

If the lines are parallel they have the same slope!

Find the slope of the line that you know:



(8-4)/(0--1) (Change in y over change in x)

Slope = 4

There the other line must have the same slope:

(8-K)/(6-4)=4

8-K=8

K=0

The slope of perpendicular line is the nagative reciprocal:

If the first line has a slope of 4 then the other one must have a slope of -1/4 to be perpendicular.

Now we do the same thing:

(8-K)/(6-4)=-1/4

8-K=-1/2

K=8.5