One side of a parallelogram has endpoints (-4, 1) and (-7, 2). The endpoints for the opposite side are (-3, 4) and (-6, 5). True False

Answer:TrueStep-by-step explanation:we know thatThe opposite sides of a parallelogram are parallel and the length of their sides is equal.step 1Find the slope of each sidewe know thatIf two lines are parallel then their slopes are the sameThe 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] comparem1=m2thereforeboth lines are parallelstep 2Find the distancethe 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] Compared1=d2Both sides have the same lengthso1) Both lines are parallel2) Both sides have the same lengththereforeThe statement is True