Question

Line l contains points (11,-1) and (-3,-11). Point P has coordinates (-1,1). Find the distance from P to l

Answer 1

For the line l:
y - y1 = [( y2 - y1 ) / ( x 2 - x 1 )] * ( x - x 1 )
y + 1 = ( -11 + 1 ) / ( - 3 - 11 ) * ( x - 11 )
y + 1 = 5/7 x - 55/7
y = 5/7 x - 55/7 - 7/7
Finally:
y = 5/7 x - 62/7
So the line that passes through P and which is perpendicular to line l has
m = - 7/5
1 = -1 * ( -7/5 ) + b
1 = 7/5 + b
b = - 2/5
Line p:
y = - 7/5 x - 2/5
Then we will find the point of intersection of lines p and l:
- 7/5 x - 2/5 = 5/7 x - 62/7 / * 35
- 49 x - 14 = 25 x - 310
x = 4
y = 5/7 * 4 - 62/7 = 6
Finally:
d = sqrt( ( 4 - (-1 ))² + ( - 6 - 1 )² ) = sqrt ( 25 + 49 ) = √ 74
Answer:
d = √ 74 ≈ 8.6