Question

1. 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

The proof is explained below :

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'.

To Prove : line 'j' is perpendicular to line 'k'.

Proof : 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 .............(1)

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

Or we can write it as n × p = -1 ...............From equation (1)

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

Hence Proved