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

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.

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