Library / /349 of 428

, 2019

Geometry Difficulty 2.4 Junior Find the answer Canada

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

IMG0

Figure for this problem

Pick one

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 $8\times4=32$ .

Figure for this problem

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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