Question

Find the equation of a line that is perpendicular to line g that contains (P, Q).


A. 3x − y = 3P − Q
B. 3x + y = Q − 3P
C. x − y = P − Q
D. x + y = Q − P

Answer 1

Determine the slope of g (visually, you can tell the rise/run)

Perpendicular —> take the opposite reciprocal of the slope —> -1/slope from the previous step

set up y - y1 = m(x-x1) using point P Q as your x1, y1

Plug in the m from the opposite reciprocal step

Re-arrange the equation if needed, to get one of the answer choices

Answer 2

alright, so here's what i've got (ive been trying to do this but im kinda confused on where i went wrong..?)


slope of line g: -1/3
perpendicular line slope: 3 (?)


y - Q = 3(x - P)

y - Q = 3x - 3P

-3x + y - Q = 3P

-3x + y = 3P + Q


Steps:

1. Given, in point-slope form
2. Distribute
3. -3x on both sides
4. +Q on both sides


what do I do next, that's not one of the options?? did I mess up?

Answer 3

nothing's incorrect, just need to play around a bit more w/ the re-arrangement step

from here:

y - Q = 3x - 3P

subtracting y from both sides
adding 3P to both sides

3x - y = 3P - Q (choice A)

Answer 4

ohhh ok, tysm!! ^