note:Parallelogram WXYZ not VWXY & I will answer the questions in the image b'cos I don't get your question.
Answers:
a.(i.)Slope of line YZ = 4/5
(ii.)Line adjacent line YZ is line YX,slope of YX =5/4
b.(i.)Length of line YZ =√41 units
(ii.)Length of line YX =√41 units
c.WXYZ is a rhombus.
Step-by-step explanation:
a.Slope=gradient(m)=(y₂-y₁)/(x₂-x₁)
(i.)m of line YZ=(y₂-y₁)/(x₂-x₁) where Y(-6,-1) & Z(-1,3)
(I believe you know what the y₂,y₁,x₂ & x₁ stand for.)
So m=(y₂-y₁)/(x₂-x₁),=(3-(-1))/(-1-(-6) =(4)/(5)=4/5
∴m of line YZ is 4/5
(ii.)m of line YX=(y₂-y₁)/(x₂-x₁) where Y(-6,-1) & X(-2,4)
So m=(y₂-y₁)/(x₂-x₁),=(4-(-1))/(-2-(-6) =(5)/(4)=5/4=1.25
∴m of line YX is 5/4
b.(i.)To find the length of line YZ,we have to express it as column vector YZ.
Vector YZ=OZ-OY,Z-Y=(-1,3)-(-6,-1)=(5,4)
Length=√x² plus y²=√5² plus 4²=√25 plus 16=√41 units
∴The length of line YZ is √41 units.
(ii.)To find the length of line YX,we have to express it as column vector YZ.
Vector YX=OX-OY,X-Y=(-2,4)-(-6,-1)=(4,5)
Length=√x² plus y²=√4² plus 5²=√16 plus 25=√41 units
∴The length of line YX is √41 units.
c.WXYZ is a rhombus.
