Find the distance of point A(2,3) measured parallel to the line x- y = 5 from the line 2x + y + 6 = 0?

1 Answer
Oct 7, 2017

Required distance is 6.13 unit

Explanation:

Slope of the line, x-y=5 or y=x-5 :. m=1 . Parallel lines

have equal slope. Let the equation of the line passing

through (2,3) and parallal to line y=x-5 is

y=mx+c or y= x+c [m=1] or 3 =2+c or c=1 since

the point (2,3) will satisfy the equation of line. Hence the

equation of the line passing through (2,3) and parallal to line

is y= x+1 . The intersection of two lines y= x+1 and

y=-2x-6 is found by solving them x+1= -2x-6 or

3x= -7 or x= -7/3 :. y= -7/3+1= -4/3 :.

Intersecting point is (-7/3,-4/3) :. Distance between

two points (2,3) and (-7/3,-4/3) is D= sqrt((2+7/3)^2+(3+4/3)^2)or

D ~~ 6.13(2dp) :. Required distance is 6.13 unit [Ans]