ABCD is a rhombus. The coordinates of A and C are (3,6) and (-1,2) respectively. Find equation of diagonal BD and prove that 2 diagonals are

Question

ABCD is a rhombus. The coordinates of A and C are (3,6) and (-1,2) respectively. Find equation of diagonal BD and prove that 2 diagonals are perpendicular to each other.

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Kaylee 7 months 2021-10-15T21:55:24+00:00 2 Answers 0 views 0

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    0
    2021-10-15T21:56:29+00:00

    Answer:please mark me as brainliest

    Step-by-step explanation:

    Step-by-step explanation:

    Given:

    Here ABCD is a rhombus. The coordinates are A(3,6) and C(-1,2).

    In rhombus, diagonals bisect each other perpendicularly.

    Let the slope of the diagonal BD =

    Slope of the given diagonal AC =  =  = 1.

    Slope of the given diagonal AC = {6-2}/{3-(-1)} = {4}/{4} = 1.

    ∴ m2*1=-1

    ∴ m_2 = -1

    ∴ Now mid point of AC is the point of bisecting.

    So the midpoint of AC =  =(1,4)

    Now,equation of the line BD

    ⇒ (y-y1) = m2(x-x1)

    ⇒ (y−4)=−1 (x−1)

    ⇒ (y−4)=−x+1

    ⇒ x+y−5=0.

    Hence  the equation of BD is x+y−5=0.

    0
    2021-10-15T21:56:56+00:00

    Answer:

    Step-by-step explanation:

    __________________________________________________

    We know that the diagonals of a rhombus bisect at right angles.

    AC ⊥ BD

    Hence the slope of AC is

    Slope of AC

    Slope of BD

    =

    O passes through BD

    O is also the midpoint of A and C

    Let O be x,y

    Midpoint formula:

    Equation of BD

    The equation of BD is :

    Hope it helps you

    Mark as brainliest pls

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