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TSI Math: Writing the Equation for a Line's Bisector 3 Views


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Description:

A line has endpoints A (0, 6) and B (-2,-10). Which of the following is the correct equation of the perpendicular bisector of this line?


Transcript

00:02

All right sy mash members another one Ah line has

00:04

en points a zero six and be at negative too

00:09

Negative ten Which of the following is the correct equation

00:12

for the perpendicular by sector of this line Cool So

00:21

uh well let's See Get that camera ready and make

00:23

sure it's got plenty of battery left because we're going

00:26

on a hunt Were hunting for a line which if

00:28

you consider getting a poor grade a matter of life

00:30

and death can be as dangerous as hunting lion All

00:33

right find this particular line were given a few clues

00:36

We're told the line is the perpendicular by sector of

00:38

a line within point So six and negative too negative

00:40

ten which is really all the information we need Because

00:43

we'll be able to find its slope here pretty easily

00:45

The line is the perpendicular by sector of line segment

00:48

a bee So its slope will be the negative reciprocal

00:51

of the slope of a bee Let's find that slope

00:54

first and we've got the whole why to money is

00:57

why one over x human sex One thing that's what

00:59

it looks like six minus eight Ten over zero money

01:01

thing to its sixteen over two or eight Voila The

01:04

negative reciprocal of aid is negative One eighth All right

01:09

so we can get rid of a and we can

01:11

get rid of sea right off the bat And actually

01:14

we can get rid of dia's Wells is not negative

01:16

So just by process of elimination we're kind of there

01:19

already But let's keep going Now that we have our

01:21

slope i really have to make sure that the line

01:23

passes through the mid point of a b to find

01:26

the midpoint of baby We'll use another one of our

01:29

trusted formulas The midpoint formula Okay so here it is

01:33

Ah this ugly thing here and we get what is

01:35

that Quantities europe listening to over to you And then

01:38

six plus minus ten answering for over two And all

01:42

that boils down Teo what is that Negative one Negative

01:45

too We need a line that passes through the point

01:47

negative one negative too and has a slope of negative

01:50

one eighth which we can easily find by plugging in

01:53

the x and y value right there Plus the slope

01:56

into the y equals mx plus b thing So that

01:58

gives us negative too is a negative one Eighth time

02:01

to think of one plus b or negative too is

02:04

when a plus b bringing the one eighth over there

02:06

on the far side And we get negative Seventeen Eight

02:10

is be so Our final equation is y equals negative

02:13

one eighth axe minus seventeen over eight And yeah that's 00:02:16.32 --> [endTime] Just be we're done for shmoop

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