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Problem 346

Geometry Difficulty 2.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2019

Line segments $PQ$ and $RS$ intersect as shown. What is the value of $x+y$ ?

Pick one

Official solution

The width of rectangle $PQRS$ is the horizontal distance between points $P$ and $Q$ (or points $S$ and $R$ ), since these points have equal $y$ -coordinates.

This distance is equal to the difference between their $x$ -coordinates or $4-(-4)=8$ .

Similarly, the height of rectangle $PQRS$ is equal the vertical distance between points $S$ and $P$ (or points $R$ and $Q$ ), since these points have equal $x$ -coordinates.

This distance is equal to the difference between their $y$ -coordinates or $2-(-2)=4$ .

The area of rectangle $PQRS$ is $8\times4=32$ .

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