CAT 2000 — QA Question 41
Basics of QuadrilateralsEasy
ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC?
Answer & solution
Correct answer: x + y = –1
x + y = –1
- B
x – y = –1
- C
x + y = 1
- D
None of the above
Solution
Equation of line AD is x + y = 1.
∴ AD intersects x-axis at (1, 0) and y-axis at (0, 1).
ABCD is a rhombus, with diagonals AC and BD intersecting at origin.
The four vertices are (1, 0), (0, 1), (−1, 0) and (0, −1).
Since AD pass through (1, 0) and (0, 1), BC passed through (−1, 0) and (0, −1).
Equation of BC
i.e. x + y = −1
Hence, option (a).