Question

if (1,5) and (-3,-1) are the coordinates of vertices A and C respectively of rhombus ABCD find the equation of the diagonal BD

Answer 1

hope this helps you....

Answer 2

Answer:

The equation of the diagonal BD is 2x+3y-4=0.

Step-by-step explanation:

The coordinates of vertices A and C are (1,5) and (-3,-1) respectively.

ABCD is a rhombus.

The diagonals of a rhombus bisects each other and perpendicular on each other.

Midpoint of AC is

$(\frac{1-3}{2},\frac{5-1}{2})=(-1,2)$

It measn point (-1,2) lies on BD.

The slope of AC,

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-5}{-3-1}=\frac{-6}{-4}=\frac{3}{2}$

The product of slopes of two perpendicular lines is -1.

$m_1\times m_2=-1$

$\frac{3}{2}\times m_2=-1$

$m_2=-\frac{2}{3}$

The slope of BD is $-\frac{2}{3}$.

The equation of BD is

$y-y_1=m(x-x_1)$

$y-2=-\frac{2}{3}(x+1)$

$3y-6=-2x-2$

$2x+3y-4=0$

Therefore the equation of the diagonal BD is 2x+3y-4=0.