# Coordinate Geometry

## 2019 National Champion

Last week the national competition concluded, and Daniel Mai from Massachusetts earned the title of MATHCOUNTS National Champion. Let’s look at some of the problems he had to solve on the way to the top!

**Sprint #14**

Two opposite vertices of a certain square are located at (1, 6) and (−3, 1). If the line *y* = *mx* divides this square into two regions of equal area, what is the value of *m*? Express your answer as a common fraction.

## Final Countdown

On Sunday, May 12th, 224 middle-school math students participated in the written rounds of the 2019 Raytheon MATHCOUNTS National Competition. On Monday, May 13th, the top 12 competitors will go head to head in the National Countdown Round to determine the 2019 MATHCOUNTS National Champion. Let’s solve a few problems from the 2018 National Countdown Round.

**2018 National Countdown #21**

In square units, what is the area of the triangle with vertices P(−2, 1), Q(3, 8) and R(9, 3)? Express your answer as a decimal to the nearest tenth.

## Fly a Kite

Molly has sketched a design for her new kite on a coordinate grid. The sides of her quadrilateral kite design are given by the equations *y* = (2/3)*x* + 30, *y* = (−2/3)*x* + 50, *y* = −2*x* + 30 and *y* = 2*x* – 30. How many square units are in the area of Molly’s design?

## MATHCOUNTS Valentine

On some graph paper, graph the following segments:

*y* = *x*, for 0 ≤ *x* ≤ 2*y* = 2*x* − 2, for 2 ≤ *x* ≤ 3*x* = 3, for 4 ≤ *y* ≤ 6*y* = −*x* + 9, for 2 ≤ *x* ≤ 3*y* = 7, for 1 ≤ *x* ≤ 2*y* = *x* + 6, for 0 ≤ *x* ≤ 1

Now reflect each of the segments over the *y*-axis. What popular shape have you drawn?