Here, we have to find the value of x such that the lines through the points (- 2, 6) and (x, 8) is perpendicular to the line through the points (3, - 3) and (5, - 9).
Let's find out the slope of the line through the points (3, - 3) and (5, - 9).
As we know that, the slope of the line joining the points
(x1,y1) and
(x2,y2) is:
m= Here,
x1=3,y1=−3,x2=5,y2=−9 ⇒m1==−3 ∵ The lines through the points (- 2, 6) and (x, 8) is perpendicular to the line through the points (3, - 3) and (5, - 9)
So, let the slope of line through the points (- 2, 6) and (x, 8) be
m2 ⇒−3×m2=−1 ⇒m2=1∕3 So, the slope of the line through the points (- 2, 6) and (x, 8) is 1/3
⇒= ⇒x+2=6 ⇒x=4 Hence, option B is the correct answer.