Question

Find the distance of the point (2 3) from the line 2x-3y+9=0 measured along the line 2x-2y+5=0

Answer 1

we have to find the distance of the point (2,3) from the line 2x - 3y + 9 = 0 measured along the line 2x - 2y + 5 = 0 .

solution : solve given equations

2x - 3y + 9 = 0 ------- (1)

2x - 2y + 5 = 0 ----- (2)

from equations (1) and (2) we get,

(2x - 3y + 9) - (2x - 2y + 5) = 0

⇒-3y + 2y + 9 - 5 = 0

⇒y = 4

and x = (3y - 9)/2 = (3 × 4 - 9)/2 = 1.5

now intersecting point is (1.5, 4)

so the distance between (1.5, 4) and (2, 3) is √{(1.5 - 2)² + (4 - 3)²}

= √{(0.5)² + (1)²}

= √(0.25 + 1)

= √5/2

Therefore the distance of the point (2,3) from the line 2x - 3y + 9 = 0 measured along the line 2x - 2y + 5 = 0 is √5/2 unit .