Find 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:
Consider the line passing through (2,3) and parallel to x−y=5 to x−y=c
c=x−y=>c=2−3=−1
Now this intersects line 2x+y+6=0 at some point and distance between this point and (2,3) is the required distance.
Solving for x−y+1=0 and 2x+y+6=0
3x+7=0=>x=
3
−7
and y=
3
−4
Distance between (2,3)and(
3
−7
,
3
−4
)is
(2+
3
7
)
2
+(3+
3
4
)
2
=
(
3
13
)
2
+(
3
13
)
2
=
3
13
2
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