Difference between revisions of "2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 10"
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== Problem == | == Problem == | ||
| − | Let <math>A,B,C</math> and <math>D</math> be points in the Cartesian plane each a distance <math>1</math> from the origin <math>(0,0)</math>. We define addition of points in the plane componentwise (If <math>P = (p_x,p_y)</math> and <math>Q = (q_x,q_y)</math>, then <math>P + Q = (p_x + q_x,p_y + q_y))</math>. Show that <math>A + B + C + D = (0,0)</math> if and only if <math>A,B,C</math> and <math>D</math> are the vertices of a rectangle | + | Let <math>A,B,C</math> and <math>D</math> be points in the Cartesian plane each a distance <math>1</math> from the origin <math>(0,0)</math>. We define addition of points in the plane componentwise (If <math>P = (p_x,p_y)</math> and <math>Q = (q_x,q_y)</math>, then <math>P + Q = (p_x + q_x,p_y + q_y))</math>. Show that <math>A + B + C + D = (0,0)</math> if and only if <math>A,B,C</math> and <math>D</math> are the vertices of a rectangle. |
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== Solution== | == Solution== | ||
Latest revision as of 09:03, 22 July 2024
Problem
Let 
and 
be points in the Cartesian plane each a distance 
from the origin 
. We define addition of points in the plane componentwise (If 
and 
, then 
. Show that 
if and only if and are the vertices of a rectangle.
Solution
See also
| 2018 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNM-PNM Problems and Solutions | ||
