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In the xy-plane, the line y = k is the perpendicular bisector of the l 09 Feb 2015, 02:59
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D
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65% (hard)

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63% (02:50) correct 37% (02:44) wrong based on 140 sessions

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In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = h is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-h, -k), then what are the coordinates of the point P?

A. (-5h, -5k)
B. (-3h, -3k)
C. (2h, 2k)
D. (3h, 3k)
E. (5h, 5k)
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D
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In the xy-plane, the line y = k is the perpendicular bisector of the l 09 Feb 2015, 08:47
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TARGET730
In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = h is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-h, -k), then what are the coordinates of the point P?

A. (-5h, -5k)
B. (-3h, -3k)
C. (2h, 2k)
D. (3h, 3k)
E. (5h, 5k)

ans D..

firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-h, -k), so R is at a distance of 2h from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4h and coord (3h,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3h,3k)..
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In the xy-plane, the line y = k is the perpendicular bisector of the l 30 Jun 2015, 07:10
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Any solutions to the correct answer?
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In the xy-plane, the line y = k is the perpendicular bisector of the l 30 Jun 2015, 07:36
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jayanthjanardhan
Any solutions to the correct answer?

Hi ,
the correct answer is D and the solution given above is for D only but its a typo error and by mistake i have written it as C

firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-h, -k), so R is at a distance of 2h from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4h and coord (3h,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3h,3k). ans D
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In the xy-plane, the line y = k is the perpendicular bisector of the l 30 Jun 2015, 08:13
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chetan, thanks for ur response. However, i am having tough time visualising the lines and the perpendicular bisectors. Is it possible for u to show it on the graph?
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In the xy-plane, the line y = k is the perpendicular bisector of the l Updated on: 30 Jun 2015, 12:10
Originally posted by ENGRTOMBA2018 on 30 Jun 2015, 08:45.
Last edited by ENGRTOMBA2018 on 30 Jun 2015, 12:10, edited 2 times in total.
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jayanthjanardhan
chetan, thanks for ur response. However, i am having tough time visualising the lines and the perpendicular bisectors. Is it possible for u to show it on the graph?

Assume that h >0 and k>0 (this assumption does not negate anything in the question stem!)

Now start with point R: This will lie in the 3rd Quadrant . The coordinates of this point are (-h,-k).

Follow, the information to calculate the coordinates for Q and then finally for P to get the correct answer. Make sure to remember that perpendicular bisectors bisect (or divide into 2 equal parts). Thus, OP = OQ and QT = TR in the attached figure.

Another way to look at this problem is to assume certain values of h and k and then do what the questions says. You will end up with the same answer.
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6-30-15 11-43-41 AM.jpg
6-30-15 11-43-41 AM.jpg [ 28.34 KiB | Viewed 6872 times ]

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In the xy-plane, the line y = k is the perpendicular bisector of the l 30 Jun 2015, 08:47
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jayanthjanardhan
chetan, thanks for ur response. However, i am having tough time visualising the lines and the perpendicular bisectors. Is it possible for u to show it on the graph?

Hi,
it has been correctly transformed on the graph above ..
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In the xy-plane, the line y = k is the perpendicular bisector of the l 30 Jun 2015, 19:49
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awesome!...thanks a lot guys!
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In the xy-plane, the line y = k is the perpendicular bisector of the l Updated on: 09 Nov 2016, 20:35
Originally posted by SW4 on 09 Nov 2016, 12:56.
Last edited by Kurtosis on 09 Nov 2016, 20:35, edited 1 time in total.
Topic Merged. Refer to the above discussions
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In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = h is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-h, -k), then what are the coordinates of the point P?

A) (-5h, -5k)
B) (-3h, -3k)
C) (2h, 2k)
D) (3h, 3k)
E) (5h, 5k)
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In the xy-plane, the line y = k is the perpendicular bisector of the l 09 Jan 2017, 21:53
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So I just used real values. A lot less confusing. Assumed that R has an x-coordinate of -2. So if 2 is bisecting QR and R has has an x coordinate of -2. So the x co-ordinate of Q should be 6. if h=2 then Q should be 3h. I quickly cross checked by having h=3 and my assumption checked out. If you look at the answer there only 1 option with the x co-ordinate as 3h since P will have the same co-ordinate.
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In the xy-plane, the line y = k is the perpendicular bisector of the l 06 May 2022, 02:51
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