Question

The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 5?

Answer 1

Given

`QS\perp US`

similar triangles = QRS and STU

Find

Missing statement .

Step-by-step explanation

As we have given

`QS\perp US`

similar triangles QRS and STU

by property of similar triangle we have ,

`(QR)/(RS)=(ST)/(TU)`

Slope of QS * Slope of US =

`(QR)/(RS)*(-TU)/(ST)`

now , substituting the property of equality

Slope of QS * Slope of US =

`(ST)/(TU)*-(TU)/(ST)`

So,

Slope of QS * Slope of US = -1

Final Answer

Missing statement =

`Slope\text{ of QS }* Slope\text{ of US =}\frac{\text{ST}}{\text{ }TU}*(-TU)/(ST)`

Correct option is A.