Question

Figure DEFG is a square. The slope of DE is 3/2. What are the slopes of EF and FG?

A. EF = -2/3 FG = -2/3
B. EF = -2/3 FG = 3/2
C. EF = 3/2 FG = 3/2
D. EF = 0 FG = 2

Answer 1

Answer: The correct option is (B)
`EF=-(2)/(3),~~FG=(3)/(2).`

Step-by-step explanation: Given that DEFG is a square in the figure shown and the slope of DE is
`(3)/(2).`

We are to find the slope of EF and FG.

We know that

the adjacent sides of a square are perpendicular to each other and the opposite sides are parallel.

Also, the product of the slopes of two perpendicular lines is -1 and the slopes of two parallel lines are equal.

Since DE and EF are adjacent sides of the square DEFG, so we must have

`\textup{slope of DE}*\textup{slope of EF}=-1\\\\\\\Rightarrow \textup{slope of EF}=-\frac{1}{\textup{slope of DE}}=-(1)/((3)/(2))=-(2)/(3).`

Now, DE and FG are opposite sides, so they must be parallel. So, we get

`\textup{slope of FG}=\textup{slope of DE}=(3)/(2).`

Thus, the slope of EF is
`-(2)/(3)` and the slope of FG is
`(3)/(2).`

Option (B) is CORRECT.

Answer 2

∵ DEFG is a square

DE is parallel to FG ⇒⇒ the slope of DE = slope of FG = 3/2

DE is perpendicular to EF
∴ the slope of EF = -1/(the slope of DE ) = -2/3

So, the correct choice is ( B. EF = -2/3 FG = 3/2)