Geometry | Og 12

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Refer page 180 of OG q no. 194

In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?

(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)

Please do not explain the OG answer. Is there any other way of doing this?

[Anurag@Gurome]

Refer page 180 of OG q no. 194

In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?

(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)

Please do not explain the OG answer. Is there any other way of doing this?

The line y = x is the perpendicular bisector of segment AB, so the point B is the mirror reflection of point A around the line y = x, so its coordinates are (3, 2). In the same way, since the x-axis is the perpendicular bisector of segment BC then the point C is the mirror reflection of point B around the x-axis, so its coordinates are (3, -2).

The correct answer is D.

[GMATGuruNY]

Refer page 180 of OG q no. 194

In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?

(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)

Please do not explain the OG answer. Is there any other way of doing this?

Just draw a picture of what is being described. A perpendicular bisector:

-- intersects at the midpoint
-- forms a right angle

Here's my rudimentary drawing:



Looking at the drawing above, we can see that point C must have a positive x-coordinate and a negative y-coordinate.
Eliminate A, B and E.
Since point C is farther to the right than point A, the x-coordinate of point C must be greater than 2.
Eliminate C.

The correct answer is D.

Check here for a similar problem:

https://www.beatthegmat.com/grockit-toug ... 74452.html