In the xy-plane, the line y = k is the perpendicular bisector of the l

Question

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)

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

chetan2u · Answer

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)..

jayanthjanardhan · Answer

Any solutions to the correct answer?

chetan2u · 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

jayanthjanardhan · Answer

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?

ENGRTOMBA2018 · Answer

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.

chetan2u · Answer

Hi,
it has been correctly transformed on the graph above ..

jayanthjanardhan · Answer

awesome!...thanks a lot guys!

SW4 · Answer

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)

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

praneet87 · Answer

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.

bumpbot · Answer

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In the xy-plane, the line y = k is the perpendicular bisector of the l

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In the xy-plane, the line y = k is the perpendicular bisector of the l

Prep Toolkit

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