Question

I really need some help with this problem, I have an exam and I cannot solve for the points.
Find the point on the line -6 x + 5 y - 6 =0 which is closest to the point ( 4, -3 ).

Answer 1

i did this for someone earlier on

Answer 2

Would you please help me with it, I've been trying to solve it for a long time but I keep getting stuck and every answer I get is wrong, its very frustrating

Answer 3

the slope of this equation is 6/5 and the
line perpendicular to it has slope -5/6 and it must pass thru the point (4, -3)
so its equation is
y -(-3) = (-5/6)(x - 4)
y+3 = (-5/6)(x - 4)
multiply thru by 6
6y + 18 = -5x + 20
6y + 5x = 2.......(a)
other equation is
-6 x + 5 y - 6 =0
rearrange
5y - 6x = 6.........(b)
WHERE THE lines of equations (a) and (b) intersect will be the shortest distance required

we now need to solve system of equations (a) and (b)

multiply (a) by 5 and (b) by 6:

30y + 25x = 10
30y - 36x = 36
subtract
61x = -26
x = -26/61
plug x into equation (a)

6y + 5* (-26/61) = 2
y = 2+ 130/61 = 252/61
The point on the line whch is the shoetest ditance

is therefore ( -26/61, 252/61)

Answer 4

the fractions are pretty messy - i might have made a mistake in solving ! but i'm sure the method is right

Answer 5

I just double checked and x is correct but y is 42/61. Thank you so so so so much for your help, i've been going nuts trying to figure out the answer and I didn't know what i was doing wrong

Answer 6

ok - yes - you are right y = 42/61 - i just checked it out on wolframalpha

Answer 7

yep - i forgot to divide 252/61 by 6 on the last line
- this gives 42/61

Answer 8

no problem you have helped me so much and your explanation was great, i wrote it all down and understood exactly how you got your answer. Thanx a million!

Answer 9

yw