2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 10

Problem

Let $A,B,C$ and $D$ be points in the Cartesian plane each a distance $1$ from the origin $(0,0)$ . We deﬁne addition of points in the plane componentwise (If $P = (p_x,p_y)$ and $Q = (q_x,q_y)$ , then $P + Q = (p_x + q_x,p_y + q_y))$ . Show that $A + B + C + D = (0,0)$ if and only if $A,B,C$ and $D$ are the vertices of a rectangle

2018 UNM-PNM Contest II (Problems • Answer Key • Resources)
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2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 10

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