Question

In a rhombus $ABCD$ the diagonals $AC$ and $BD$ intersect at the point $(3,4)$. If the point $A$ is $(1,2)$ the diagonal $BD$ has the equation

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

Answer 1

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

Given points are

$O(x,y)=(3,4)$

$A(x_1,y_1)=(1,2)$

Point C coordinates are $C(x_2,y_2)=?$

Now,

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

$x_2=5,y_2=6$

So, equation of diagonal is

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

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

$\Rightarrow y-2=\frac{4}{4}(x-1)$

$\Rightarrow y-2=x-1$

$\Rightarrow x-1-y+2=0$

$\Rightarrow x-y+1=0$

Hence, this is the answer.