Graph G has a line of symmetry of x = 5/2. Graph G passes through th

Question

Graph G has a line of symmetry of x = –5/2. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?

(A) –8
(B) –7
(C) –5
(D) –4
(E) 2

iamdp · Accepted Answer

Hi 
the logic applicable here in the attached pic

aniteshgmat1101 · Answer

Answer is A.
Graph is symmetrical in the both sides of line x = -5/2. So, the graph is constituted with the points which is at same distance from the line x = -5/2 both the sides of it.
 Having that in mind, given x-coordinate is at a distance of 5.5 units from the line x = -5/2, then another x-coordinat must be at the same distance but on the other side of the line, which should be (-5/2 + ( - 5.5)) = -8 units.

lipsi18 · Answer

Line of symmetry is X=-2.5; one point is (3,3)
Right side distance =2.5+3(distance from origin) = 5.5; therefore Left side distance should be same from line of symmetry =5.5; 
therefore left side co-ordinate=5.5+ 2.5(distance from origin) = 8; as the X coordinate is in 2nd quadrant hence -8 
Therefore answer is A

Thanks

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

The line of symmetry is x = –2.5. The point (3, 3) is 3 – (–2.5) = 5.5 to the right of this line of symmetry. It’s reflection must be 5.5 units to the left of the line of symmetry, so (–2.5) – (5.5) = –8 is the x-coordinate.

Answer = (A)

OreoShake · Answer

Can someone please tell me what is a line of symmetry and the laws governing this concept? From what I can reason from the explainations, it looks like the line between a line and its relfection line.

ajdse22 · Answer

Visually, the term symmetry implies that another side is a mirror reflection of one side. In coordinate geometry for example a graph of y=x^2 is a symmetric around point (0,0). Why so? This is because if we take x = -5 or +5, the outcome is same i.e. 25. Another example is absolute value function.

Putting differently, if we know that the graph is symmetric around x=0, and we know that graph passes by 5,25 , then we also know that the line will again pass y=25 at another point which is opposite to x=0 but has the same distance of 5. So the new point is -5. 
The question above is testing symmetry using this concept.
Hope this helps you

Graph G has a line of symmetry of x = 5/2. Graph G passes through th

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Graph G has a line of symmetry of x = 5/2. Graph G passes through th

Prep Toolkit

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