Question

Provide reasons for the proof. Given line h is parallel to line k. line j is perpendicular to line h. Prove line j is perpendicular to line k

Answer 1

Answer: Provided.

Step-by-step explanation: We are given two lines 'h' and 'k' which are parallel to each other. Also, there is another line 'j' that is perpendicular to line 'h'.

We are to prove that line 'j' is perpendicular to line 'k'.

Let, m, n and p be the slopes of lines 'h', 'k' and 'j' respectively.

Now, since line 'h' and 'k' are parallel, so their slopes will be equal. i.e., m = n.

Also, lines 'h' and 'j' are perpendicular, so the product of their slopes is -1. i.e.,

m×p = -1.

Hence, we can write from the above two relations

n×p = -1.

Thus, the line 'j' is perpendicular to line 'k'.

Proved.