Axis-Aligned Distance on the Coordinate Plane

How the lesson starts: Axis-Aligned Distance on the Coordinate Plane

Zip lines at Camp Maple
Welcome to Camp Maple, zip-line champ! Counselor Max strings zip lines between trees on a big map grid. Every line runs straight across, or straight up and down. Before he buys cable, Max needs to know how long each line is. Let's measure with coordinates!
Same x: straight up
Tree A is at (2, 3). Tree B is at (2, 9). Both have x = 2, so the zip line runs straight up and down. Why compare the y's? Because only y changes along the line. 9 − 3 = 6, so the line is 6 units long. Count the squares to check!
Across zero
Tree C is at (−4, 6) and tree D is at (5, 6). They share y = 6, so look at the x's. From −4 to zero is 4. From zero to 5 is 5. So the line is 4 + 5 = 9 units. Watch out: 5 − 4 = 1 is wrong! The trees sit on opposite sides of zero.