Question

Good morning, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.

Answer 1

6.

(a)

The slope for the side AB is:

`\begin{gathered} A=(-5,-4)=(x1,y1) \\ B=(5,-2)=(x2,y2) \\ m_(AB)=(y2-y1)/(x2-x1)=(-2-(-4))/(5-(-5))=(2)/(10)=(1)/(5)=0.2 \end{gathered}`

The slope for the side BC is:

`\begin{gathered} B=(5,-2)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_(BC)=(6-(-2))/(7-5)=(8)/(2)=4 \end{gathered}`

The slope for the side DC is:

`\begin{gathered} D=(-3,4)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_(DC)=(y2-y1)/(x2-x1)=(6-4)/(7-(-3))=(2)/(10)=(1)/(5)=0.2 \end{gathered}`

And the slope for AD is:

`\begin{gathered} A=(-5,-4)=(x1,y1) \\ D=(-3,4)=(x2,y2) \\ m_(AD)=(4-(-4))/(-3-(-5))=(8)/(2)=4 \end{gathered}`

(b) According to the previous results:

`\begin{gathered} m_(AB)=m_(DC) \\ so \\ m_(AB)\parallel m_(DC) \end{gathered}`
`\begin{gathered} m_(BC)=m_(AD) \\ so\colon \\ m_(BC)\parallel m_(AD) \end{gathered}`

(c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram