Distance on the Coordinate Plane

What you’ll learn

• Main idea: straight-line distance on a grid = hypotenuse of a right triangle whose legs are horizontal and vertical separations.
• Build the triangle: move horizontally, then vertically; the right angle is at the corner point, not at A or B.
• Show arithmetic in order: square each leg, add, then square root (example: $8^2 = 64$, $6^2 = 36$, $64 + 36 = 100$, $\sqrt{100} = 10$).
• Then name legs $\Delta x$ and $\Delta y$; the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ is the same steps in one line.
• Also in this unit: city-block $|x_2-x_1|+|y_2-y_1|$, map scale, perimeter sums, round to the nearest tenth at the end.