Question

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?

• A. (A) 2x + y = 0
• B. (B) 2x - y = 0
• C. (C) x + 2y = 0
• D. (D) x - 2y = 0

Answer 1

Answer: (A)

(A) 2x + y = 0

Answer 2

Explanation:
Concept:The equation of a line passing through the point (x1,y1) and having the slope ' m ' is given as:y−y1=m⋅(x−x1)Given: The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2).So, the diagonal AC passes through the origin,As we know that, the slope of the line joining the points (x1,y1) and (x2,y2) is: m=y2−y1x2−x1The slope of line AC is given by2−04−0=12In square ABCD, the diagonals AC and BD are perpendicular to each other.⇒ Slope of AC× slope of BD=−1So, the slope of BD is - 2 .As we know that, the equation of a line passing through the point (x1,y1) and having the slope ' m ' is given as:y−y1=m⋅(x−x1)The equation of BD whose slope is - 2 and passes through origin is given by:y−0=(−2)⋅(x−0)⇒2x+y=0Hence, the correct option is (A).