Question

A perpendicular bisector to 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.

A(-4,5) and B (8,9)
A(2,4) and B (-8,6)
A(5,4) and B (7,2)
A(2,9) and B (-4,3)
A(3,-2) and B (9,-12)
A(4,10) and B (8,12)

Answer 1

To find perpendicular bisector first find the midpoint of the points A and B by using the section formula.
Then find the slope of the perpendicular bisector(You can find the slope of line segment AB).
Then using the slope of the perpendicular bisector and the midpoint of AB(which lies on it) u can find its equation.
Then it should be pretty straightforward to find their y-intercepts.

Answer 2

so what's the slope for line AB?

Answer 3

ok ok im here

Answer 4

ok so what's the slope for line AB?

Answer 5

I got 1/3 when I solved it.

Answer 6

did u get that

Answer 7

how did you get 1/3 because when you subtract 8 minus -4 isn't it 4 or somethin?

Answer 8

its 12
8-(-4)=12

Answer 9

9-5=4 so slope is 1/3

Answer 10

oh its ok. OH so after i find all the slopes what do i do after that?

Answer 11

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 12

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

Answer 13

yea, the y-intercept

Answer 14

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

Answer 15

how would i do that?

Answer 16

you have to distribute the 1/3 first

Answer 17

distribute the 1/3 to the 4

Answer 18

how do you get the 5 to the other side?

Answer 19

subtraction?

Answer 20

I got to Y-5=1/3x+4/3

Answer 21

how did you get the 4/3? I just want to know how to work out the first one so i get the others correct.

Answer 22

srry i need some time to solve this im getting confused

Answer 23

@phi

Answer 24

@Sachintha

Answer 25

its ok don't worry.

Answer 26

ok let me see if anyone else can help

Answer 27

@Vocaloid

Answer 28

@tigerlover

Answer 29

@nickj123

Answer 30

@jtug6

Answer 31

alright but thanks for helping! :)

Answer 32

hope these guys and ladys can help srry again that i cant help m8

Answer 33

This is for Plato, you need to miss only one

Answer 34

we want the equation of the *perpendicular bisector*
i.e. perpendicular to the line segment AB
if the slope of AB is m
the slope of the perpendicular is -1/m
("flip" the slope, then multiply by -1)

for example, for the first A,B pair
A(-4,5) and B (8,9)

you get a slope m = 1/3
now "flip" that fraction to get 3/1 or 3
then multiply by -1 to get -3

-3 is the slope of the perpendicular.

Answer 35

next, you need a point on the perpendicular bisector.
by definition, one point is the point exactly in between A and B
to find that point, I would find the average of the x value of A and the x value of B
and do the same for the y values.

Answer 36

For example, with
A(-4,5) and B (8,9)

the x value of the midpoint is (-4+8)/2 = 4/2 = 2
the y value is (5+9)/2 = 14/2 = 7
so (2,7) is a point on the perpendicular bisector.

we can now find the equation of the line of this perpendicular bisector.
one way is write
y = m x + b
fill in m (which is -3)
y = -3 x + b
now fill in x and y for a point on the line. in other words, we use (2,7):
7 = -3*2 + b
7 = -6+b
add 6 to both sides:
6+7 = 6-6+b
13= b
that means the y-intercept is 13
finally, we have the equation.

y = -3x + 13

so the first pair has a y-intercept of 13

we have to do all that work for each pair of A, B. (Gack!)

Answer 37

@phi I am trying to form a general equation for the perpendicular bisector. But, I am getting the wrong equation. -_-

Answer 38

I got a messy one. It's hardly worth using
\[b= \frac{ (A_x^2 +A_y^2) - (B_x^2 +B_y^2)}{2(A_y-B_y)} \]

Answer 39

which formula do i use? Its match and match so if i get one wrong it messes up everything

Answer 40

I would first: find the slope of each A/B pair.
can you do that ?

Answer 41

ok ill try,gonna take me some time

Answer 42

1. 1/3
2 -10/2
3 2/-2
4. -6/-6 6.4/2
5. 6/-10

Answer 43

is that right? Can someone confirm

Answer 44

almost. it looks like you did change in x divided by change in y
which is upside down.

Answer 45

this problem has to be done carefully. so please fix those slopes.

Answer 46

Point P is an arbitrary position on the perpendicular bisector and C is the mid point of A and B.

Gradient of line AB = \(\Large\frac{y_2-y_1}{x_2-x_1}\)

Gradient of line PC = \(-\Large\frac{x_2-x_1}{y_2-y_1}\)

I got the equation of line PC as,
\(y-y_3=-\Large\frac{x_2-x_1}{y_2-y_1}\normalsize(x_3-x)\)

I can't figure out what I have done wrong. >_<