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

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Answer 1 · 2017-10-07T12:52:49

Required distance is #6.13# unit

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]