A line passes through (2,2) and cuts a triangle of area 9 from the first quadrant. The sum of all possible values for the slope of such a line, is?

A) -2.5
B) -2
C) -1.5
D) -1

1 Answer
Oct 30, 2017

Answer is (A).

Explanation:

Let the slope of the line be m. As it passes through (2,2), its equattion is

y-2=m(x-2) or y=mx-2m+2

Now, area of triangle in such a case is half the product of x-intercept and y-intercept.

x-intercept is given by putting y=0 i.e. mx-2m+2=0 or x=(2m-2)/m and y-intercept is given by putting x=0 i.e. y=-2m+2.

Hence, if area of triangle is A

2A=(-2m+2)(2m-2)/m=(-4m^2+8m-4)/m

or 18=(-4m^2+8m-4)/m

or 18m=-4m^2+8m-4

or 4m^2+10m+4=0

As in a quadratic equation ax^2+bx+c=0, sum of roots is -b/a

sum of slopes is -10/4=-2.5 and answer is (A).

graph{(x+2y-6)(y+2x-6)=0 [-1, 13, -0.5, 6.5]}