Question

ABCD is a rhombus. The coordinates of A and C are (3,6) & (-1,2) respectively. Write down the equation of BD

Answer 1

hope this helps you....

Answer 2

Hence  the equation of BD is x+y−5=0.

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 = $m_2$

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

∴ $m_2\times1=-1$

∴ $m_2 = -1$

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

So the midpoint of AC = $(\frac{3+(-1)}{2} ,\frac{6+2}{2} )$ =(1,4)

Now,equation of the line BD

⇒ $(y-y1) = m_2(x-x1)$

⇒ (y−4)=−1 (x−1)

⇒ (y−4)=−x+1

⇒ x+y−5=0.

Hence  the equation of BD is x+y−5=0.