Question

Two lines m annd l are perpendicular to lines pand n respectively. If n amd p intersect , proove l and m also intersect .

Answer 1

See below

Explanation:

Since lines n and p intersect, they must have different slopes. Lets say they have slopes 2 and 4, as an example. They will intersect. Lines m and l are perpendicular to n and p, so their slopes will be the negative inverse of 2 and 4. That gives them slopes of -(1/2) and -(1/4). These slopes are different, so they will intersect.

The attached graph illustrates this intersection with lines having the above slopes. Lines m and l intersect at (-1,1) in this example. Lines m and l also intersect, off the graph at the top left.