Question

given the point p(-3,2) and the line 3x+4y=6, find:

the perpendicular distance between P and the give line,

the gradient of the line that is perpendicular to 3x+4y=6,
the general equation of the line that is perpendicular to 3x+4y=6

Answer 1

ok so i know how to do the perpendicular distance but i just want to know when i take it out of the absolute value sign am i suppose to say +/- my answer...

Answer 2

and what do they mean by gradient

Answer 3

and for the general equation the slope just because the negative reciprocal which is -4/3....correct?

Answer 4

gradient is a british word for slope

Answer 5

the slope of the line given is: -3/4

perp slope will be 4/3 and include the point (-3,2)

its easier to get the equation by flipping coeefs and negating the operator

Answer 6

could u help me when ur done thanks sorry

Answer 7

3x+4y=6

4x-3y = n ; fill in the point (-3,2)

-12 -6 = -18

4x -3y = -18 is the line for the perp

Answer 8

now when we solve for the point that they cross at; we get a new point tp measure a distance to

Answer 9

do we use y-y1=m(x-x1)...no? or they are not be specific when they asked for slope-intercept equation

Answer 10

oh okay

Answer 11

the general is just the flip coeffs and negate the operator

Answer 12

its a shortcut that aounts to the same as flipping the slope over and chagning the sign lol

Answer 13

what are they asking for when they say general equation?

Answer 14

3x +4y = 6
4x -3y = -18 ; Ax+By = C is the general i think

Answer 15

lol okay yeah and you use y-y1=m(x-x1) to get this form right?

Answer 16

3x +4y = 6 ; *4
4x -3y = -18 ; *-3


12x +16y = 24
-12x +9y = 54
--------------
25y = 78

y = 78/25 ; dbl chk that

Answer 17

no, I just use the equation they gave and adjusted it for the perp

Answer 18

i got 3y-4x=18

Answer 19

3x+4y=6 ;flip the numbers like this

4x +3y = n ; now change the operator like this

4x -3y = n ; now plug in the point they gave you to calibrate this

Answer 20

we got the same equations; mines just not a negative

Answer 21

\(\color{#d2477e}{\text{s}}\)\(\color{#e84c46}{\text{a}}\)\(\color{#921ad1}{\text{m}}\)\(\color{#e48a3d}{\text{e}}\)\(\color{#539458}{\text{ }}\)\(\color{#7e5517}{\text{e}}\)\(\color{#84144f}{\text{q}}\)\(\color{#e81dff}{\text{u}}\)\(\color{#cb177c}{\text{a}}\)\(\color{#bd9fb1}{\text{t}}\)\(\color{#72a77a}{\text{i}}\)\(\color{#2127e4}{\text{o}}\)\(\color{#be3cf6}{\text{n}}\)\(\color{#53ff69}{\text{s}}\)\(\color{#2a231f}{\text{;}}\)\(\color{#a1ec7c}{\text{ }}\)\(\color{#c5d2ed}{\text{m}}\)\(\color{#e1d424}{\text{i}}\)\(\color{#86bc68}{\text{n}}\)\(\color{#875bbb}{\text{e}}\)\(\color{#ee6964}{\text{s}}\)\(\color{#cc336f}{\text{ }}\)\(\color{#edf426}{\text{j}}\)\(\color{#2ff3d2}{\text{u}}\)\(\color{#616b93}{\text{s}}\)\(\color{#f832f2}{\text{t}}\)\(\color{#78447c}{\text{ }}\)\(\color{#f913d1}{\text{n}}\)\(\color{#985c62}{\text{o}}\)\(\color{#39b8a5}{\text{t}}\)\(\color{#968c55}{\text{ }}\)\(\color{#c2fd4f}{\text{n}}\)\(\color{#61de21}{\text{e}}\)\(\color{#4cd222}{\text{g}}\)\(\color{#332193}{\text{a}}\)\(\color{#3e7a63}{\text{t}}\)\(\color{#f75137}{\text{i}}\)\(\color{#e8214b}{\text{v}}\)\(\color{#362d14}{\text{e}}\)\(\color{#2d292c}{\text{}}\)

Answer 22

lol why are you using color...idk what went wrong...but @ least i got the right concept thanks so much amistre! cool colors.

Answer 23

:) its my new invention for spicing up openstudy lol

Answer 24

lol okay.stay away from the bright colors though...could cause some folks to need glasses

Answer 25

epileptic lol

Answer 26

What did you get for the perpendicular distance from the point (-3,2) and the given line?

Would it be the distance between (-3,2) and ((-54/25),(78/25))?

Answer 27

\[d=\sqrt{(-3+(54/25))^{2}+(2-(78/25))^{2}}\]
\[d=\sqrt{(21/25)^{2}+(-28/25)^{2}}=1.4\]
Is that even close?