find the distance of the point(1,2)from the straight line with slope 5 and passing through the point of intersection of - Maths - Straight Lines

Question

find the distance of the point(1,2)from the straight line with
slope 5 and passing through the point of intersection of x+2y and
x-3y=7

Shipra D. · Accepted Answer

Since, the equation x+2y is incomplete so I am assuming it to be
x+2y=2 â€‹

The intersection point of the lines x+2y=2 and x-3y=7 is    x+2y=2-(x-3y=7)____________5y=-5⇒y=-1 substituting in x+2y=2 we getx+2-1=2⇒x=4So, the point of intersection is 4, -1
The equation of a line passing through 4, -1 and having slope 5 is given asy+1=5x-4y+1=5x-20⇒5x-y=21Therefore, the distance between the point 1, 2 and the line 5x-y=2 is given by:Distance between y=mx+c and the point x1, y1=y1-mx1-cm2+1 Distance between 5x-y=21 and the point 1, 2=-2+51-2152+1=-1826=1826units

find the distance of the point(1,2)from the straight line with slope 5 and passing through the point of intersection of x+2y and x-3y=7