In the rectangular coordinate system above, the line y = x

For this question, I am confused. where do I get the position of B and C?
Thanks ...

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)

Since the line y=x is the perpendicular bisector of segment AB, then point B is the mirror reflection of point A around the line y=x, so its coordinates are (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

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 y-axis, so its coordinates are 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

Answer: D.

The question becomes much easier if you just draw a rough sketch:Now, you can simply see that only D can be the correct answer.

Answer: D.

Similar questions to practice:
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

Hope it helps.

Hi Bunuel
I solved this question with slope intercept form and took more than 2 minutes.
Can you please explain how did you conclude mirror reflection thing.
It would be really helpful if you could provide theory or link to theory which explains the concept of points and their mirror reflection with respect to lines, axes and quadrants.
Thanks

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)

Since the line y=x is the perpendicular bisector of segment AB, then point B is the mirror reflection of point A around the line y=x, so its coordinates are (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

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 y-axis, so its coordinates are 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

Answer: D.

The question becomes much easier if you just draw a rough sketch:



Now, you can simply see that only D can be the correct answer.

Answer: D.

Similar questions to practice:
https://gmatclub.com/forum/in-the-rectan ... 32646.html
https://gmatclub.com/forum/in-the-rectan ... 29932.html

Hope it helps.

Bunuel, why we didn't extend line AB more to have some other co-ordinates for B? Say, if AB cuts line xy at point P perpendicularly, then is it necessary that AP = PB?

First of all, this question is not very easy. You should be able to visualize a concept which is not very intuitive to most of us but there are a few OG questions on it. I suggest you to read up on it in the following two posts:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/04 ... ry-part-i/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/04 ... y-part-ii/

Now, coming back to this question, you are given data to find the positions of B and C.

"the line y = x is the perpendicular bisector of segment AB (not shown)"

You know that point A is (2, 3). We need the mirror image of A on y = x. Imagine drawing a line perpendicular to y = x from A. It will intersect y = x at (2.5, 2.5), a point 0.5 below and 0.5 to the right. So the point B will be 0.5 further to the right and 0.5 down giving us the coordinate (2.5 + .5, 2.5 - .5) i.e. (3, 2).

For C, you are given that
" the x-axis is the perpendicular bisector of segment BC (not shown)"

A line perpendicular to x axis will be x = 0 i.e. vertical line. So C's x coordinate will be the same as B's x coordinate. Since B is 2 above the x axis, C will be 2 below the x axis. So C will be at (3, -2)

Hi VeritasKarishma

For this blog, could you explain how did you deduce a 30-60-90 triangle from only knowing that radius of circle / hypotenuse = 2? The length of minute clock is fixed, so if I join center to number 9 and center to number 12, both lengths of both these segments will be the same. Right?