Question

Line WV is perpendicular to both line RS and line TU.

Which statement must be true about line TU?
Line TU is parallel to line RS.
Line TU is perpendicular to line RS.
Line TU has no slope.
Line TU has a slope of –5

Answer 1

Answer: The true statement is 'Line TU is parallel to line RS'.

Explanation: Since, we know that if a line is perpendicular to two different lines then these two different lines must be parallel to each other.

Here, it is given that WV is perpendicular to both lines RS and TU.

Therefore, RS must be parallel to TU.

⇒ Option (1) is correct.

Note: Option (2) 'Line TU is perpendicular to line RS' can not be possible.

Option (3) 'Line TU has no slope' is only possible if the line TU is parallel to the X-axis, which is not mentioned in the question.

So, we can not say it to be true.

Option(4) 'Line TU has a slope of –5' can be true or not.

We can find the slope of line TU if we have the equation of line TU.

Therefore, it also not necessarily true.

Answer 2

TU is parallel to line RS because both equations are perpendicular on the same line.

Hope this helps :)