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Problem 219

Geometry Difficulty 1.4 Find the answer CEMC Pascal · Canada · 2012

Points with coordinates $(1,1)$ , $(5,1)$ and $(1,7)$ are three vertices of a rectangle.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Since the given three points already form a right angle, then the fourth vertex of the rectangle must be vertically above the point $(5,1)$ and horizontally to the right of $(1,7)$ . Therefore, the $x$ -coordinate of the fourth vertex is $5$ and the $y$ -coordinate is $7$ . Thus, the coordinates of the fourth vertex are $(5,7)$ .

Figure for this problem

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.