Answer:
True
Step-by-step explanation:
we know that
The opposite sides of a parallelogram are parallel and the length of their sides is equal.
step 1
Find the slope of each side
we know that
If two lines are parallel then their slopes are the same
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
one side
[tex]A(-4,1)\ B(-7,2)[/tex]
Substitute the values
[tex]m1=\frac{2-1}{-7+4}[/tex]
[tex]m1=\frac{1}{-3}[/tex]
[tex]m1=-\frac{1}{3}[/tex]
opposite side
[tex]A(-3,4)\ B(-6,5)[/tex]
Substitute the values
[tex]m2=\frac{5-4}{-6+3}[/tex]
[tex]m2=\frac{1}{-3}[/tex]
[tex]m2=-\frac{1}{3}[/tex]
compare
m1=m2
therefore
both lines are parallel
step 2
Find the distance
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
one side
[tex]A(-4,1)\ B(-7,2)[/tex]
Substitute the values
[tex]d1=\sqrt{(2-1)^{2}+(-7+4)^{2}}[/tex]
[tex]d1=\sqrt{(1)^{2}+(-3)^{2}}[/tex]
[tex]d1=\sqrt{10}\ units[/tex]
opposite side
[tex]A(-3,4)\ B(-6,5)[/tex]
Substitute the values
[tex]d2=\sqrt{(5-4)^{2}+(-6+3)^{2}}[/tex]
[tex]d2=\sqrt{(1)^{2}+(-3)^{2}}[/tex]
[tex]d2=\sqrt{10}\ units[/tex]
Compare
d1=d2
Both sides have the same length
so
1) Both lines are parallel
2) Both sides have the same length
therefore
The statement is True
