If PQ=RQ, then which of the following must be true ?

6 Answers

• Anonymous

  1 month ago

  There are two definitions of a perpendicular bisector:

  (i) A line that passes through the midpoint and is perpendicular to the line

  (ii) A line that contains all points that are equidistant from the two endpoints of the line.

  Using definition (ii), the second statement is true.

  I hope this helps!

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• Raymond

  1 month ago

  Since you do not state that R is distinct from P, then it is possible that point Q is exactly at the same place as point P.

  In such a case, then, all 4 statements could be false.

  Let the point P be at the origin

  P(0, 0)

  Let the point Q be one unit to the right on the x-axis

  Q(1, 0)

  Let the point R be at the origin

  R(0, 0)

  [there is no rule that forbids two points to be at the same spot, unless you state that the points must be distinct]

  Then the distance PQ = 1.

  The distance QR is also 1.

  PQ = RQ

  1) Q is not the midpoint of PR (the mid point of PR would be (0, 0))

  2) The perpendicular of PR is undefined.

  3) PQ + QR = 1 + 1 (distances are never negative); while PR = 0

  HOWEVER, if you mean PQ and QR as vectors, then the vector QR is (-1 0) while PQ = (+1 0) and, in such as case, statement number 3 would be true.

  4) Q(1, 0) is not between P(0, 0) and R(0, 0)

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• G

  1 month ago

  I am guessing more than one can be true, because the way you have written this question, that is the case.

  If Q is the midpoint of PR, then PQ must be the same length as QR. So 1, 3, and 4 are true.

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• Anonymous

  1 month ago

  . . . . . . . . . . . . . . . |. . . . . . . . . . . . . . . .

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  . . . . . . . . . . . . . . . Q. . . . . . . . . . . . . . . .

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  P ————————–M——————————R

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  . . . . . . . . . . . . . . . |. . . . . . . . . . . . . . . .

  This is the drawing most suitable for your problem. M is the middle of PR. MQ is the perpendicular bisector of PR.

  The correct answer is (2) because any point on the perpendicular bisector is at the same distance from P as from R. And because of that we have that the answers (1), (3) and (4) are not true for any point Q that respects your assumption that PQ = QR.

  PS: sorry for the incomplete drawing, but it’s not my fault… PR is longer; R is on the right side.

  1
• Iggy Rocko

  1 month ago

  Answer is (2).

  2
• Romila

  1 month ago

  NOne

  0