find the distance of intersection of line from other lines
Answers
Answer:
= 130/(17√29)
Step-by-step explanation:
find the distance of intersection of line from other lines
2x - 3y + 5 = 0
3x + 4y = 0
To find intersection Point
3 * Eq1 - 2*eq2
=> 6x - 9y + 15 - ( 6x + 8y) = 0
=> -17y + 15 = 0
=> y = 15/17
3x + 4(15/17) = 0
=> x = -20/17
intersection Point ( -20/17 , 15/17)
To find Minimum distance from 5x - 2y = 0
Distance Should be ⊥
5x - 2y = 0
=> y = 2.5x => slope = 2.5
Slope of Perpendicular line should be
-1/2.5 = - 2/5
y = (-2/5)x + c
=> 5y = -2x + 5c
x = -20/17 & Y = 15/17
=> 75/17 = 40/17 + 5c
=> 35/17 = 5c
=> 5y = -2x + 35/17
=> 85y = -34x + 35
=> 34x + 85 y = 35
& 5x - 2y = 0
5 * eq 1 - 34 * eq2
=> 425y + 68 y = 175
=> y = 175/493
x = 70/493
Distance between ( -20/17 , 15/17) & ( 70/493 , 175/493)
(-580/493 , 435/17) & ( 70/493 , 175/493)
= √ (-650/493)² + (260/493)²
= (1/493)√490100
= (130√29)/(17 * 29)
= 130/(17√29)