3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners of the soccer goal are located at O(0,0,0), A(0,0, 2.5), B(7.5,0,2.5) and C(7.5,0,0). The goalkeeper stands at point G, which is the midpoint of the line segment OC. All mea- surements are in metres. A B C (a) Determine the coordinates of points G and P. (b) Determine PA and PC. Which point A or C is closer to P? Justify your answer.

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The
corners of the soccer goal are located at O(0,0,0), A(0, 0, 2.5), B(7.5,0, 2.5) and C(7.5,0, 0).
The goalkeeper stands at point G, which is the midpoint of the line segment OC. All mea-
surements are in metres.
A
P
(a) Determine the coordinates of points G and P.
(b) Determine PA and PC. Which point A or C is closer to P? Justify your answer.
(c) The player P kicks the ball and it is stopped by the goalkeeper at a point S which is 9
metres along the line segment from P to A. Determine the coordinates of point S.
Transcribed Image Text:3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners of the soccer goal are located at O(0,0,0), A(0, 0, 2.5), B(7.5,0, 2.5) and C(7.5,0, 0). The goalkeeper stands at point G, which is the midpoint of the line segment OC. All mea- surements are in metres. A P (a) Determine the coordinates of points G and P. (b) Determine PA and PC. Which point A or C is closer to P? Justify your answer. (c) The player P kicks the ball and it is stopped by the goalkeeper at a point S which is 9 metres along the line segment from P to A. Determine the coordinates of point S.
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