A line passes through #(2,2)# and cuts a triangle of area #9 " units"^2# 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
A) -2.5
B) -2
C) -1.5
D) -1
2 Answers
Sum of slopes is
Explanation:
A line passing through point
or
or
or
Observe that such a line forming a triangle in
and its
and hence area of triangle so formed is
or
or
or
or
i.e.
Hence sum of slopes is
and lines are
graph{(x+2y-6)(2x+y-6)=0 [-6.69, 13.31, -2.62, 7.38]}
Explanation:
Let, the X-intercept and Y-intercept of the line, say
point
Clearly,
Observe that,
of which, the lengths of the sides making the right angle are
Hence, the area of the right-triangle is
Knowing that,
Then,
These give