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A line passes through (2,2) and cuts a triangle of area 9 square units from the first quadrant . The sum of all possible values for the slope of such a line,is [OPTIONS]: A.-2.5 B.-2 C.-1.5 D.-1 P.S.The answer is A.-2.5.Just tell me how.

 
A line passes through (2,2) and cuts a triangle of area 9 square units from the first quadrant . The sum of all possible values for the slope of such a line,is
[OPTIONS]:
A.-2.5
B.-2
C.-1.5
D.-1
 
P.S.The answer is A.-2.5.Just tell me how.

Grade:11

1 Answers

Kartik
13 Points
6 years ago
x/x1+y/y1=1  (passes through 2,2)
2/x1+2/y1=1
2(x1+y1)=x1y1                   equ. 1
now area,
1/2(x1y1)=9
x1y1=18              equ.    2
put equ.2 in equ. 1
x1+y1=9          equ. 3
solving equ. 3 and equ. 2 we get
(x1y1) gives (6,3), (3,6)
slope = -2,-1/2
sum of slope =-2.5    Answer
 

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