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Points P, Q, and R lie in the coordinate plane. If P = (l, 5), Q = (1
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04 Jan 2023, 07:41
04 Jan 2023, 07:41
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63% (01:25) wrong based on 72 sessions
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Points P, Q, and R lie in the coordinate plane. If P = (1, 5), Q = (1, 1), and R = (7, y), how many different integer values for y could be chosen to form Triangle PQR, such that none of the angles in Triangle PQR is greater than 900?
(A) 0
(B) 3
(C ) 5
(D ) 7
(E) It cannot be determined from the information given.
(A) 0
(B) 3
(C ) 5
(D ) 7
(E) It cannot be determined from the information given.
Re: Points P, Q, and R lie in the coordinate plane. If P = (l, 5), Q = (1
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30 Jan 2023, 16:33
30 Jan 2023, 16:33
Expert Reply
OE
An obtuse angle is an angle with degree measure higher than 90°. As the following diagram shows, if y is greater than 5 or less than 1, it will cause triangle PQR to have an obtuse angle. Therefore, y must be an integer between 1 and 5, inclusive:
GRE (2).jpg [ 53.74 KiB | Viewed 4619 times ]
An obtuse angle is an angle with degree measure higher than 90°. As the following diagram shows, if y is greater than 5 or less than 1, it will cause triangle PQR to have an obtuse angle. Therefore, y must be an integer between 1 and 5, inclusive:
Attachment:
GRE (2).jpg [ 53.74 KiB | Viewed 4619 times ]
Re: Points P, Q, and R lie in the coordinate plane. If P = (l, 5), Q = (1
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22 Aug 2023, 19:02
22 Aug 2023, 19:02
2
If P = (1, 5), Q = (1, 1), and R = (7, y), how many different integer values for y could be chosen to form Triangle PQR, such that none of the angles in Triangle PQR is greater than 90degree?
Note that x coordinate of P and Q is same i.e., 1
and y coordinate of Q is 1 and P is 5
thus, to keep the angles less than equal to 90degree, we can chose integer value of y from 1 to 5 i.e., 5 integer values.
for y = 1, angle PQR is 90 degree and for y = 5 angle QPR is 90 degree.
Answer C
Note that x coordinate of P and Q is same i.e., 1
and y coordinate of Q is 1 and P is 5
thus, to keep the angles less than equal to 90degree, we can chose integer value of y from 1 to 5 i.e., 5 integer values.
for y = 1, angle PQR is 90 degree and for y = 5 angle QPR is 90 degree.
Answer C
