Question

The points A(7 , 3) and C (0, -4) are two opposite vertices of rhombus ABCD. Find the equation of the diagonal BD.

Answer 1

Diagonals of a rhombus bisect each other and intersect at 90°

Slope AC = -4-3÷0-7 = 1

Slope AC × Slope BD = -1

Slope BD = -1

Mid point of AC = 7+0÷2,3-4÷2 = 7/2,-1/2

Slope = -1

Point = 7/2,-1/2

y - y1 = m(x - x1)

y+1/2 = -x + 7/2

x + y -3 =0

HOPE THIS ANSWER HELPS PLZ MARK AS BRAINLIEST.

Answer 2

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

Step-by-step explanation:

Given:

• The given points of two opposite vertices of a rhombus $ABCD$ are $A(7 , 3)$ and $C (0, -4)$.

To find:

• To find the equation of the diagonal $BD$.

Formula used:

The formula required to find the slope of AC is $m_{=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

The formula required to find the equation of BD is $y-y_{1} =m(x-x_{1} )$

Solution:

Step 1:

At first, we have to find the slope of $AC$

$m_{=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

$m=\frac{-4-3}{0-7}$

$m=\frac{-7}{-7}$

$m=1$

BD is ⊥ to AC

hence, $m=-1$

Step 2:

The midpoint of $AC$ is $E$.

The midpoint of E's coordinates are $(\frac{7+0}{2},\frac{3-4}{2} )$

we get $(\frac{7}{2} ,\frac{-1}{2} )$

let us considered $(x_{1} ,y_{1} )= (\frac{7}{2} ,\frac{-1}{2} )$

now find the equation of $BD$

$y-y_{1} =m(x-x_{1} )$

$y+\frac{1}{2} =-1(x-\frac{7}{2} )$

$\frac{2y+1}{2} =\frac{-2x+7}{2}$

$2(2y+1)=2(-2x+7)$

$4y+2=-4x+14$

combine the equation

$-4x+14-4y-2=0$

$-4x-4y+12=0$

now divide the equation by -3

$x+y-3=0$

hence, $x+y-3=0$is the equation for the diagonal BD.