Question

Write an equation for the line perpendicular to XY that contains point Z.

XY: 3x+2y=-6, Z(3,2)

Answer 1

What you want to do is get the equation in the form y =..... In this case you just take 3x from both sides and divide by 2, leaving you with y = -3/2x - 3. That means the gradient is -3/2. The gradient of any perpendicular line is -1/gradient of first line, giving you 2/3. Then put the gradient and your points x,y (3,2) into the equation y-y1 = m(x-x1). You should get y-2=2/3(x-3), which ends up being y=2/3x

Answer 2

Okay so with the coordinates (since I have to show my work and I'm kinda confused too) what do you do with the coordinates because 3 and 2 are both in the equation and coordinates?

Answer 3

@iGreen can you help me? ;;

Answer 4

I got it now but what's a gradient and why is it -1?

Answer 5

Gradient is the slope. And it's not -1 sorry, it's -1 divided by the gradient of the first line.

Answer 6

Ohh~ So why did we divide by -1?

Answer 7

We didn't divide by minus 1

Answer 8

Ohh then what did we do? o.O

Answer 9

We did -1/(-3/2) which is 2/3

Answer 10

\[\frac{ -1 }{ \frac{ -3 }{ 2 } }\] Sorry, is that a little more clear?

Answer 11

Yeah it is so if I had a question like y=3/4x+22 and the coordinates are (12,8) I just put them in point slope form too?

Answer 12

Sorry, I'm not sure what point slope form is

Answer 13

Isn't that the one with y-y1=m(x-x1)?

Answer 14

You'll need to find the gradient of the perpendicular first, which would be -4/3 and then yeah, put it into that equation with 12 and 8.

Answer 15

Oh my gosh *moment of revelation* I GOT IT!! Thank you so much!!

Answer 16

You're very welcome :)