Posted by **Kate** on Saturday, June 13, 2009 at 10:05am.

Consider the points (3, –1) and

(9, 2).

(a) State the midpoint of the line segment with the given endpoints.

(b) Find the distance between the points. Show some work. Give the exact answer (involving a radical), and also an approximation to three decimal places.

(c) Find the slope of the line passing through the two given points. Show some work.

- Algebra -
**Reiny**, Saturday, June 13, 2009 at 10:16am
I will give you the formulas for the problems,

for any two points (a,b) and (c,d)

1. Midpoint = ((a+c)/2,(b+d)/2)

2. Distance between the two points

= √[(a-c)^2 + (b-d)^2]

3. slope = (b-d)/(a-c)

compare (a,b) and (c,d) with your given points and evaluate.

Let me know what you get

- Algebra -
**Anonymous**, Saturday, June 13, 2009 at 10:17am
This has got to be in your text book!

The midpoint is the average x and the average y

Xav = (3+9)/2 = 6

Yav = (-1+2)/2 = 1/2

so

(6 , 1/2)

d^2 = [(Y2-Y1)^2 + (X2-X1)^2 ]

= [ 3^2 + 6^2 ]

= [ 9 + 36 }

= 45

so

d = sqrt 45 = 3 sqrt 5

slope = (Y2-Y1) / (X2-X1)

I think you can carry that division out

- Algebra -
**Kate**, Saturday, June 13, 2009 at 10:28am
(x1 + x2)/2, y1 + y2)/2 =

3+9/2 = 12/2 = 6

-1+2/2 = 1/2 = .05

This is what I got for the mid point. is this correct? I got 6 for the first set of numbers, and .05 for the second. How do I determine the mid point?

- Algebra -
**Kate**, Saturday, June 13, 2009 at 10:33am
I think I figured it out. The answer can contain a fraction along with whole numbers. So i guess the mid point would be (6,.05) correct?

- Algebra -
**Reiny**, Saturday, June 13, 2009 at 10:37am
"Anonymous" already gave you the answer.

why don't you just replace the values ?

you started with ...

((x1 + x2)/2, (y1 + y2)/2) , notice I corrected your "bracket errors"

= ((3+9)/2,(-1+2)/2)

= (6,1/2)

you had .05

1/2 is .5 not .05

- Algebra -
**Kate**, Saturday, June 13, 2009 at 10:42am
oops I misplaced the decimal. So yea (6,0.5) is the solution I came up with.

- Algebra -
**Kate**, Saturday, June 13, 2009 at 10:45am
Now I will work on the distance and slope parts. Hopefully they will be correct to!

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