Question

given: $overleftrightarrow{qs}perpoverleftrightarrow{us}$ and $\triangle qrssim\triangle stu$ prove: slope of $overleftrightarrow{qs}\times$ slope of $overleftrightarrow{us}=-1$

statements	reasons
2. $\frac{qr}{rs}=\frac{st}{tu}$	property of similar triangles
3. slope of $overleftrightarrow{qs}=\frac{qr}{rs}$ slope of $overleftrightarrow{us}=-\frac{tu}{st}$	definition of slope
4. slope of $overleftrightarrow{qs}\times$ slope of $overleftrightarrow{us}=\frac{qr}{rs}\times-\frac{tu}{st}$	multiplying the slopes
5.	substitution property of equality
6. slope of $overleftrightarrow{qs}\times$ slope of $overleftrightarrow{us}=-1$	simplifying the right side

the table shows the proof of the relationship between the slopes of two perpendicular lines. what is the missing statement in step 5?
a. slope of $overleftrightarrow{qs}\times(-$ slope of $overleftrightarrow{us}) = 1$
b. slope of $overleftrightarrow{qs}\times$ slope of $overleftrightarrow{us}=1$
c. slope of $overleftrightarrow{qs}\times$ slope of $overleftrightarrow{us}=\frac{st}{tu}\times\frac{tu}{st}$
d. slope of $overleftrightarrow{qs}\times$ slope of $overleftrightarrow{us}=\frac{st}{tu}\times-\frac{st}{tu}$

Explanation:

Step1: Recall step 2

From step 2, we have $\frac{QR}{RS}=\frac{ST}{TU}$.

Step2: Analyze step 4

In step 4, we have slope of $\overleftrightarrow{QS}\times$ slope of $\overleftrightarrow{US}=\frac{QR}{RS}\times-\frac{TU}{ST}$.

Step3: Substitute

Substitute $\frac{QR}{RS}=\frac{ST}{TU}$ into the product - of - slopes formula in step 4. So, slope of $\overleftrightarrow{QS}\times$ slope of $\overleftrightarrow{US}=\frac{ST}{TU}\times-\frac{TU}{ST}$.

Answer:

D. slope of $\overleftrightarrow{QS}\times$ slope of $\overleftrightarrow{US}=\frac{ST}{TU}\times-\frac{TU}{ST}$