Find the distance of the point (2,5) from the 3x+y+4=0 measured parallel to a line having slope 3/4 - Maths - Straight Lines

Question

Find the distance of the point (2,5) from the 3x+y+4=0 measured
parallel to a line having slope 3/4

Ajanta Trivedi · Accepted Answer

let P (2,5) be the point from which we are measuring the distance the equation of the line passing through the point P and having slope 3/4 is: $y - 5 = \frac{3}{4} (x - 2) 4 y - 20 = 3 x - 6 3 x - 4 y + 14 = 0 (1)$ now let this line intersect the given line 3x+y+4=0 (2)at point A therefore the required distance will be AP now we will find the intersection point of (1) and (2)

3x-4y+14=0 3x+y+4=0 -5y+10=0 i e y=2 substitute the value of y in (2) 3x+2+4=0â‡’3x+6=0â‡’x=-2 therefore the coordinates of the point A is (-2,2) distance $A P = \sqrt{(- 2 - 2)^{2} + (2 - 5)^{2}} = \sqrt{4^{2} + 3^{2}} = \sqrt{16 + 9} = \sqrt{25}$ hence AP= 5 units

Find the distance of the point (2,5) from the 3x+y+4=0 measured parallel to a line having slope 3/4.