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) Calculations: Given: The point of intersection of diagonals of a square
ABCD is at the originand 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= The slope of line
AC is givenby
= In square
ABCD, the diagonals
AC and
BD are perpendicular to each other.
⇒ Slope of
AC× slope of
BD=−1 So, the slope of
BD is
−2.
As we know that, the equation of a line passing through thepoint
(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=0 Hence, the correctoption is 1 .