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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

  • calculista:

    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

Parallelogram: Congruent Sides Of Parallelogram 44% OFF

Parallelogram: Congruent Sides Of Parallelogram 44% OFF

Source: www.congress-intercultural.eu

Parallelogram With Diagonals

Parallelogram With Diagonals

Source: mungfali.com

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