All the points lying inside the triangle with coordinates #(1,3),(5,0),(-1,2)# satisfy?

A) #3x+2y >= 0#
B)#2x+y-13 >=0#
C)#2x-3y-12 <=0#
D)#-2x+y>=0#

1 Answer
CW
Oct 5, 2017

#"Option " A and "Option " C#

Explanation:

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A) Substitute #(1,3),(5,0) and (-1,2)# in #3x+2y >= 0#
# 3(1)+2(3)=9 >= 0#
# 3(5)+2(0)=15 >= 0#
#3(-1)+2(2)=1 >=0#
As #(1,3),(5,0) and (-1,2)# satisfy #3x+2y >= 0#,
Option #A# is correct (see Fig 1)

B) Similarly, since #(1,3),(5,0) and (-1,2)# do not satisfy #2x+y-13>=0#,
Option #B# is not correct. (see Fig 2)

C) Similarly, since #(1,3),(5,0) and (-1,2)# satisfy #2x-3y-12<=0#,
Option #C# is correct. (see Fig 3)

D) Similarly, since #(5,0)# does not satisfy #-2x+y>=0#,
Option #D# is not correct. (see Fig 4)

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