Question

ABCD is a rhombus with AC and BD intersecting at the origin. The equation of side AD is $x + y = 1$. What is the equation of BC?

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

Hint:

For parallel lines, slope is identical. For symmetry about origin, change the intercept sign.

Answer 1

The Correct Option is B

In a rhombus, opposite sides are parallel. If AD has equation $x + y = 1$, then BC is parallel $\Rightarrow$ slope same. Also BC is opposite and shifted such that origin is midpoint of both diagonals $\Rightarrow$ BC must have same slope and pass through point symmetric to AD w.r.t origin. Hence intercept is negative of AD’s intercept: $x + y = -1$. \[ \boxed{x + y = -1} \]