Question

Line L contains points (1, -3) and (0, 4). Point H has coordinates (-1, 3). Find the distance from Point H to Line L.

So far from here, I have done most of the work, and I have the answer but I can't manage to recreate it, and I need to show my work (I guessed it and got it right.) I currently have all the way up to the distance formula but I can't go forward from there!

Answer 1

Just by the way to let you know the distance formula I have is \[\sqrt{(3/25 + 1)^2 + (79/25 - 3)^2}\]

Answer 2

but my calculator is not cooperating

Answer 3

update i must have mathematically died because ^ but without the root is 1.28 and not \[\sqrt{32}\]

Answer 4

rip. the problem is that with the line that point isnt perfectly aligned with the line so that x2 won't work. i have to first find the equation of the first line then make a perpandicular line with the point, then find the coinciding point then finally using the distance formula.

Answer 5

@bibby that wont work because i have to find the perpandicular point so that won't work :(((

Answer 6

yes perpandicular with one of the points being point h

Answer 7

the slope is 1/7 and that messies up everything, but I kept going with it and ended up getting the point (3/25, 79/25) and kept going and that ended up being really wrong @bibby

Answer 8

use symbolab.com to help u find the answer (im good with middle school geometry sowwie)

Answer 9

Hint:

So first find the general form of the line between (1,-3) and (0,4), in the form Ax+By+C=0.
Then calculate the distance from point P(-1,3) using the formula above.

Answer 10

and that becomes y=1/7x+22/7

Answer 11

1/7x+22/7=-49/7x+28/7

Answer 12

which becomes 50/7x=6/7

Answer 13

which becomes 50=6x which becomes 50x=6 which becomes x=3/25

Answer 14

and from there it only gets messier.

Answer 15

i give up bye

Answer 16

@bibby @literallyjian
The slope m=(y2-y1)/(x2-x1)=(4-(-3))/(0-1)=7/(-1)=-7
substituting in (y-y1)=m(x-x1) gives
y-0=-7(x-4), or
y=-7x+4
(check: -7(0)+4=4, so (0,4) is on the line. and -7(1)+4=-3, so (1,-3) is also on the line.)
Change to general form:
7x+y-4=0, or Ax+By+C=0
with A=7, B=1, C=-4
Substitute in the formula in the drawing I posted earlier, and put P(a,b)=(-1,3) to find the distance.