Question

In a rhombus ABCD the diagonals AC and BD intersect at the point (3,4) if the point the (1,2) then the equation of the diagonal BD is :

• A. $x-y+1=0$
• B. $x+y-7=0$
• C. $2x+y-10=0$
• D. $x-2y+5=0$

Answer 1

The correct option is A $x-y+1=0$

We have,

ABCD is a rhombus

AC and BD be the diagonal

Mid point of both diagonal is $(x,y)=(3,4)$

Then point $B(x_1,y_1)=(1,2)$

So, we know that,

$(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$(3,4)=(\frac{1+x_2}{2},\frac{2+y_2}{2})$

$3=\frac{1+x_2}{2},4=\frac{2+y_2}{2}$

$1+x_2=6,8=2+y_2$

$x_2=5,y_2=6$

So,

$D(x_2,y_2)=(5,6)$

Then equation of diagonal $BD$

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-2=\frac{6-2}{5-1}(x-1)$

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

$y-2=x-1$

$x-y+1=0$

Hence, this is the answer.