Question

"Ok, so I have a question.
A perpendicular bisector to "Line AB" is drawn through point C and extended to point D.

Arrange the pairs of points in order of the y-intercepts of their corresponding perpendicular bisectors, starting with the smallest and ending with the largest."

I am good with finding slope (I think) , I'm good there, but finding the Y-intercept and plugging it all into Y=mx+b has had me frustrated.

A(-4,5) B(8,9) Help me solve this one, so I can figure the rest out please? I would greatly appreciate the help. Thank you.

Answer 1

uhm so, let's find the equation for line ab first? I don't know what they are referring to by pairs of points, but I can definitely get you the lines

Answer 2

so what's the slope for line AB?

Answer 3

I got 1/3 when I solved it.

Answer 4

good, so now, you know the slope for your line now we just need to plug that into point-slope form to get the eq for the line

Answer 5

so right now we are at Y=1/3x+b right? Now we are solving for the Y-intercept?

Answer 6

oh, no, do you know point-slope equation?

Answer 7

I think I missed that equation. Or miss interpreted it for Y=mx+b.

Answer 8

\[y-y_0=m(x-x_0)\] your point that you know is \( (x_0,y_0)\)

Answer 9

Ah ok. so Y-5=1/3(x+4)?

Answer 10

that equation is called the point slope equation. If you don't know intercept, it's the easiest way to get the line

Answer 11

Ok.

Answer 12

yep, so now just solve for y and you'll get your intercept.

Answer 13

Y=1/3x+9? I think I did this last night, but got confused on how to execute it. Did I get it right?

Answer 14

you have to distribute the 1/3 first

Answer 15

it's close, but you forgot to distribute the 1/3 to the 4

Answer 16

you will get a fractional intercept I believe

Answer 17

Ok, I got to Y-5=1/3x+4/3. I'm not sure how to to distribute the 5, and I left my calculator at school this weekend, so I am a bit stuck at that...

Answer 18

well you don't distribute the 5

Answer 19

how do you get the 5 to the other side?

Answer 20

Yes, that's what I meant.

Answer 21

I its suppose to be simple, but I kind for got how to do that.

Answer 22

how do you undo minus 5?

Answer 23

Add it to both sides.

Answer 24

right, so that's how you get the -5 from the left to the right

Answer 25

Ok, so with that is the Y-intercept like 6 1/3? I guess it doesn't really matter how I simplify, as I just need to know the general number of it, but still. Is that basically the correct answer? Y=1/3x+6 1/3?

Answer 26

yup

Answer 27

now for the perpendicular line, the slope will be the opposite of the reciprocal for your line. So, what is the reciprocal of 1/3?

Answer 28

3 right?

Answer 29

yea, and what is the opposite of 3?

Answer 30

-3 correct?

Answer 31

yep, so now you need a point

Answer 32

that's where the perpendicular BISECTOR part comes in

Answer 33

Ok, so am I just basically looking for a set of coordinates with the opposite reciprocal at this point?

Answer 34

no, you need the point of intersection

Answer 35

For where the bisector intercepts line AB?

Answer 36

yea

Answer 37

How do I figure out where the bisector intercepts?

Answer 38

well, what does bisector mean?

Answer 39

That it divides down the middle. Do I use the distance formula for this part?

Answer 40

no, midpoint formula

Answer 41

it's easier

Answer 42

Ah ok. Whats the formula for that again?

Answer 43

google that one, or purplemath it

Answer 44

Ok. Anything after figuring out the Midpoint?

Answer 45

plug it into point slope again and you have you two lines. I don't know what they want from you after that. The phrasing on this question doesn't make much sense to me

Answer 46

Would a screenshot bring more light?

Answer 47

probably

Answer 48

Here.

Answer 49

oh god... that's awful. So you have to write the eq for every perp bisector then order them by y-intercept...

Answer 50

Apparently so.

Answer 51

I am so sorry. That's an evil problem

Answer 52

what grade?

Answer 53

You have no idea. This is just one of many in a sinister recovery class. I'm a senior in high school, but I got to finish this recovery class to graduate this year.

Answer 54

lol, I get that. I teach those classes. Should've passed it first time around, it's easier that way

Answer 55

I don't usually blame the teacher.. but I blame the teacher. One kid complained how he was getting a better grade in his honors class, and it dropped to a C with her... But yeah, I know. Should have done it first time around, oh well.

Answer 56

Anyway, thank you! Atleast I can get this done now.

Answer 57

np, keep it going. It'll be over soon