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

Option A. Line TU is parallel to line RS is correct

Explanation:

Given : Line WV is perpendicular to Line RS and Line TU

Now, if line WV is perpendicular to line RS

Then if slope of line WV is m and slope of line RS is n

⇒ m × n = -1 .......(1)

Also, if line WV is perpendicular to line TU

Then if slope of line WV is m and slope of line RS is p

⇒ m × p = -1 ....(2)

From equation (1) and equation (2)

We get, m × n = m × p

⇒ n = p

So, Slope of line RS is equal to Slope of line TU

And if slope of two lines are equal to each other then the lines are parallel to each other.

⇒ Line TU is parallel to Line RS

Therefore, Option A. is correct

Answer 2

The sketch of the three lines is shown in the diagram below

If the line WV perpendicular to both RS and TU, that means that RS and TU are parallel to each other

Correct answer: A