Question

Can you please help me

Answer 1

Let:

A=(-4,10)=(x1,y1)

B=(-8,1)=(x2,y2)

`m_(AB)=(1-10)/(-8-(-4))=(-9)/(-4)=(9)/(4)=2.25`

C=(-5,7)=(x1',y1')

D=(-2,4)=(x2',y2')

`m_(CD)=(y2^(\prime)-y1^(\prime))/(x2^(\prime)-x1^(\prime))=(4-7)/(-2-(-5))=-(3)/(3)=-1`

E=(2,-3)=(x1'',y1'')

F=(6,-7)=(x2'',y2'')

`m_(EF)=(y2^(\doubleprime)-y1^(\doubleprime))/(x2^(\doubleprime)-x1^(\doubleprime))=(-7-(-3))/(6-2)=(-4)/(4)=-1`

Since:

`\begin{gathered} m_(CD)=m_(EF) \\ -1=-1 \end{gathered}`

The lines CD and EF are parallel