the distance of the point (3,5) from the line 2x +3y - 14 = 0 measured parallel to the line x - 2y = 1 is ?
a) 7/ root 5
b) 7/ root 13
c) root 5
d) root 13
It should be c) root 5.
As the distance is supposed to measured along a line parallel to x-2y-1 =0, the slope of the lines will be the same.
therefore, 2y=x-1, and y = x/2 -1/2.
Acc slope-intercept form slope, m = 1/2.
Now we can get the equation of the line on which (3,5) lies.
Using slope intercept form we get the equation as : x-2y+7 = 0. NOw to get the intersection of this line with the original line, we solve the two equations to get x = 1 and y=4.
Now using distance formula we find the distance between these two points i.e. (3,5) and (1,4) which is equal to root 5.