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555-605 (Medium)|   Geometry|      
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Raisakatyal
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In the xy-plane, point P has coordinates (4,3). If circle O has its ce 26 May 2023, 02:22
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

69% (02:03) correct 31% (01:49) wrong based on 80 sessions

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In the xy-plane, point P has coordinates (4,3). If circle O has its center at the origin and passes through the coordinates (0,10), then what is the greatest distance from point P to a point on circle O.

A. 5
B. 9
C. 15
D. 16
E. 20
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C
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Raisakatyal
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In the xy-plane, point P has coordinates (4,3). If circle O has its ce 26 May 2023, 02:23
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Can someone pls explain this question in detail. (with a figure if possible).
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tryingtoaimhigher
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In the xy-plane, point P has coordinates (4,3). If circle O has its ce 07 Sep 2023, 17:02
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Hi, would be grateful if someone could post an explanation for this question. Thanks.
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In the xy-plane, point P has coordinates (4,3). If circle O has its ce 08 Sep 2023, 13:46
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Raisakatyal
In the xy-plane, point P has coordinates (4,3). If circle O has its center at the origin and passes through the coordinates (0,10), then what is the greatest distance from point P to a point on circle O.

A. 5
B. 9
C. 15
D. 16
E. 20
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Let’s draw a figure and mark the known points.

radius = √[(0 – 0)² + (10 – 0)²] = 10 [This is the distance between the point (0,10), which is on the circle, and the origin, which is the center of the circle.]

Next, draw a diameter of the circle through point P, which has coordinates (4,3), and denote the endpoint of this diameter that is farther from point P by Q.

We can see that point Q is the farthest point on the circle from point P.

PO = √[(4 – 0)² + (3 – 0)²] = √(25) = 5
OQ = radius = 10

PQ = 5 + 10 = 15

Answer: C
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