Let’s draw the rhombus first for better understanding.
DIAGRAM
$\text{AD}: x+y = 1 \longrightarrow (1)$
- put, $x=0 \Rightarrow y=1$
- put, $y=0 \Rightarrow x=1$
Now, equation of $\text{BC}: y-0 = \frac{0-(-1)}{-1-0}(x+1)$
$\Rightarrow y= -(x+1)$
$\Rightarrow \boxed{x+y=-1}$
(OR)
$y-(-1) = \frac{0-(-1)}{-1-0}(x-0)$
$\Rightarrow y+1 = -x$
$\Rightarrow \boxed{x+y=-1}$
Correct Answer $: \text{A}$
$\text{PS}$
- Given two points $(x_{1},y_{1})$ and $(x_{2},y_{2}),$ the line passing through these two point is:
$$\boxed{y-y_{1} = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}(x- x_{1})}$$
$$\text{(OR)}$$
$$\boxed{y-y_{2} = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}(x- x_{2})}$$
- Properties of rhombus: A rhombus is a quadrilateral whose sides are all equal.