Question

Indicate the equation of the given line in standard form.

The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

Answer 1

@apoorvk

Answer 2

i know the mid-point is (3 , -1).

Answer 3

yeah great, now can you find out the equation of the line passing through those two points?

Answer 4

y+1=1/2(x-3)

is that right?

Answer 5

or wrong equation?

Answer 6

well the slope of the line perpendicular to d line joinin d points is 2 nd nt 1/2

Answer 7

sorry. what?

Answer 8

the equation is (y+1)=2(x-3)

Answer 9

but i thought the slope was -1/2... y2-y1/x2-x1 so -2-0/5-1 is -2/4 which is -1/2

Answer 10

that is the slope of d line joinin d points.any line perpendicular 2 dis line will have a slope which is d negative reciprocal of d earlier slope! the product of d slopes of perpendicular lines are always = -1

Answer 11

okay. (sorry i just get confused when people don't speak english.)

so the slope of the perpendicular line is 2?

Answer 12

Ohkay, what you did first was right, Mr. Sailor!

Answer 13

The equation of the line passing through the two points is exactly what you found out.

Now, express that in standard form, i.e. 'ax + by + c = 0', can you?

Answer 14

y+1=1/2(x-3)

this? or

(y+1)=2(x-3)

Answer 15

The first one. That is:
\[y + 1 = \frac 1 2 (x-3)\]

Answer 16

2y + 2 = 2x - 6
2y = 2x - 8
y = x - 4

is that right so far?

Answer 17

yes, no?

Answer 18

Umm, you sent that '2' in the denominator to the other side, okay, but then you have
2y + 2 = x- 3

right? :D

Answer 19

ah. yes. okay. i see.

so then
2y + 2 = x - 3
2y = x - 5
-x + 2y= -5

i feel i went wrong somewhere. :/

Answer 20

x - 2y = -5?

Answer 21

yeah great now!
Now now..

For a straight line "ax + by = c", the equation of the line perpendicular to it is:
"bx - ay = k"

where 'k' is another constant.

So, what do you think would be the equation of the perpendicular line in terms of 'x', 'y' and 'k'?

Answer 22

No, sailor, the r[previous one was correct
that is '- x + 2y = -5'

Answer 23

wait wait wait. where did the a and the b come from?

Answer 24

It's the standard equation of a straight line!

Answer 25

compare and find out 'a' and 'b' in in your case.

Answer 26

oh my brain. okay.

-1 is a and 2 is b?

Answer 27

and k is -5?

Answer 28

great!
no the constants are different, 'k' and is not the same as 'c'.

so, what would be the equation of the perpendicular line if it's "bx-ay =k"

forget 'k' for a moment.

Answer 29

I mean include 'k' in the equation but write it just as 'k'.

Answer 30

2x+y=k

Answer 31

great!

now this line passes through that midpoint (3,-1).
so that means this point satisfies the equation of the perpendicular line.
So substitute and find out 'k' from this, can you?

Answer 32

2*3 + 1 =k

k=7

Answer 33

yeahh!!
so you got 'k'

now substitute it in the equation for the perpendicular line that we had obtained, i.e.:
2x+y=k

that would be your answer!

Answer 34

2x+y=7

thanks!

just wondering, is there a faster way of doing this?

Answer 35

yeah, do this without my help, and practice it a bit, this is basically just a two step process if you notice.

Answer 36

alright:) thanks again

Answer 37

No worries ;)