we know that
Parallelogram is a quadrilateral with opposite sides parallel and equal in length
so
[tex]FI=GH\\FG=IH[/tex]
[tex]AD=BC\\AB=DC[/tex]
we have
[tex]F(-6,-1) \\G(-1,-1)\\H(-2,-4)\\I(-7,-4)\\A(3,8)\\D(1,2)[/tex]
Step 1
Find the distance FI
we know that
the distance between two points is equal to the formula
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]F(-6,-1) \\I(-7,-4)[/tex]
substitute the values
[tex]d=\sqrt{(-4+1)^{2}+(-7+6)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-1)^{2}}[/tex]
[tex]dFI=\sqrt{10}\ units[/tex]
Step 2
Find the distance FG
we know that
the distance between two points is equal to the formula
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]F(-6,-1) \\G(-1,-1)[/tex]
substitute the values
[tex]d=\sqrt{(-1+1)^{2}+(-1+6)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(5)^{2}}[/tex]
[tex]dFG=5\ units[/tex]
Step 3
Find the distance AD
we know that
the distance between two points is equal to the formula
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(3,8)\\D(1,2)[/tex]
substitute the values
[tex]d=\sqrt{(2-8)^{2}+(1-3)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(-2)^{2}}[/tex]
[tex]dAD=\sqrt{40}\ units[/tex]
Step 4
Find the scale factor
we know that
the scale factor is equal to
[tex]scale\ factor=\frac{dAD}{dFI}[/tex]
we have
[tex]dFI=\sqrt{10}\ units[/tex]
[tex]dAD=\sqrt{40}\ units[/tex]
substitute the values
[tex]scale\ factor=\frac{\sqrt{40}}{\sqrt{10}}=2[/tex]
Step 5
Find the coordinate of point B
we know that
the length side of the segment AB is equal to
[tex]dAB=scale\ factor*dFG[/tex]
we have
[tex]scale\ factor=2[/tex]
[tex]dFG=5\ units[/tex]
substitutes
[tex]dAB=2*5=10\ units[/tex]
the x-coordinate of point B is equal to the x-coordinate of point A plus the distance AB
[tex]Bx=Ax+dAB[/tex]
where
Bx------> is the x-coordinate of point B
Ax-------> is the x-coordinate of point A
dAB------> distance AB
susbtitute
[tex]Bx=3+10=13[/tex]
the y-coordinate of point B is equal to the y-coordinate of point A
[tex]By=8[/tex]
therefore
the coordinate of point B is [tex](13,8)[/tex]
the answer is the option
[tex](13,8)[/tex]
