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Q. If one of the diagonals of the square is along the line x=2y and one of the vertices...

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user8235304 | Student, Grade 11 | Valedictorian

Posted July 24, 2013 at 1:24 AM via web

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Q. If one of the diagonals of the square is along the line x=2y and one of the vertices is (3,0),then the sides through this vertex are given by the equation:-

A) `y-3x + 9=0,3y+x - 3=0`

B) `y+3x + 9=0,3y+x - 3=0`

C) `y-3x + 9=0,3y-x + 3=0`

D) `y-3x + 3=0,3y+x + 9=0`

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted July 24, 2013 at 1:50 AM (Answer #1)

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Test the equations using the point (3, 0).

Begin by testing the first equation in each set.

A and C:
The line for the equation y - 3x + 9 = 0 includes the point (3, 0).  You can check this using substitution.

y - 3x + 9 = 0
0 - 3 * 3 + 9 = 0
0 - 9 + 9 = 0
0 = 0 (true)

B:
The line for the equation y + 3x + 9 = 0 does not include the point (3, 0).  You can check this using substitution.

y + 3x + 9 = 0
0 + 3 * 3 + 9 = 0
0 + 9 + 9 = 0
18 = 0 (false)

D:
The line for the equation y - 3x + 3 = 0 does not include the point (3, 0).  You can check this using substitution.

y - 3x + 3 = 0
0 - 3 * 3 + 3 = 0
0 - 9 + 3 = 0
-6 = 0 (false)

Now your choices are narrowed down to either A or C.  Test the second equation for both choices.

A:
3y + x - 3 = 0
3 * 0 + 3 - 3 = 0
0 + 0 = 0
0 = 0 (true)

C:
3y - x + 3 = 0
3 * 0 - 3 + 3 = 0
0 - 3 + 3 = 0
0 = 0 (true)

Both A and C are correct.

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