Given: l║m, m ∉ l, m ∉ m. the distance between point m and line l is 4 cm, the distance between m and line m is 3 cm. find the distance between parallel lines l and m. (consider two possible positions for point m)

The distance between m and I can 7 cm or 1 cm.

Explanation:

According to the question, distance between point M and line m= 3 cm

Distance between point M and line I=4 cm

Since, according to the given data there can be two cases possible.

M can be a point between these two lines

In this case the distance between m and I = distance between point M and line m + distance between point M and line I=  3+4=7 cm

M can be the point above the line m(where line m is above the line I)

In this case the distance between m and I= Distance between point M and line I- distance between point M and line I= 4-3=1 cm

Note: we can not take the case in which M is the point above the line I  where line I is above the line m because in that case distance between M and m must be greater than 3 which can not be possible.  

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