you need to use the formula for the length of the perpendicular from a point and a line.
let the line be
let the point be
the perpendicular's length is .
I don't understand how they get (x + 5t, y + 3t) ? If they are perpendicular, surely it should be (x - 3t, y + 5t) or something similar?
i can help you understand that through a conversation. be sure to ask questions till you don't get the thing clearly.
here we go.
0) forget for a moment the solution they have given. we will come back to that later. produce your own solution.
1) our aim is to find the length of the perpendicular from (1,2) to the line 5x+3y+7=0.
2) now draw the point (1,2) and 5x+3y+7=0 on a graph paper or any regular paper but make the figure accurate enough.
3) now draw roughly a line passing through (1,2) and perpendicular to 5x+3y+7=0. call this line L'
4) L' will intersect 5x+3y+7=0 somewhere. (agreed?). Can you find the equation of line L'.??
5) call the point of intersection of these two lines as K.
6) Can you find K. further, can you find the distance between K and (1,2).??
I was trying to use this method earlier.
I obtained L2 (perpendicular passing through (1, 2) as y = 3x/5 + 7/5)
I then re-arranged L1 and put L1 = L2 to obtain the point (-28/17, 7/17), call this point K.
Square root ((Kx - 1)^2 + (Ky - 2)^2)
Sorry, tried to use Latex but kept getting errors!
But i did not obtain the correct answer =(
i was about to post this. well you can also see that http://myasdcommunity.com/solutions%...o%20sense.jpeg is wrong. they have found out the parametric equation of the line. that's correct. but calculation of is wrong. Our answer matches with the formula i had posted in my first post. don't worry what you have done is correct.