9D Distance & Polygons on Coordinate Plane Study Guide

Key Vocabulary

Distance — how far apart two points are. (distancia)

Polygon — a closed shape made of straight line segments (triangle, rectangle, etc.). (polígono)

Vertices — the corner points of a polygon (singular: vertex). (vértices)

Perimeter — the total distance around a shape (add all side lengths). (perímetro)

Horizontal — going left and right (same y-values). (horizontal)

Vertical — going up and down (same x-values). (vertical)

1 Check if the line is horizontal or vertical. Horizontal = same y-value. Vertical = same x-value.
2 For horizontal distance: Subtract the x-values and take the absolute value. |x₂ − x₁|
3 For vertical distance: Subtract the y-values and take the absolute value. |y₂ − y₁|
4 For perimeter: Find the length of each side, then add them all together.

Horizontal distance = |x₂ − x₁|

Vertical distance = |y₂ − y₁|

Perimeter = sum of all side lengths

Find the distance between (2, 3) and (2, −4).

Same x-value (both are 2) → vertical line.
Distance = |3 − (−4)| = |3 + 4| = |7| = 7 units

Find the distance between (−3, 5) and (4, 5).

Same y-value (both are 5) → horizontal line.
Distance = |4 − (−3)| = |4 + 3| = |7| = 7 units

Use absolute value! Distance is always positive. You cannot have negative distance.
Subtracting a negative is the same as adding: 3 − (−4) = 3 + 4 = 7.
This method only works for horizontal and vertical lines (same x or same y). For diagonal lines, you need a different method (not in 6th grade).
Perimeter means add ALL sides, not just two. Count every side of the polygon!

1. Find the distance between (1, 4) and (1, −3).

2. Find the distance between (−5, 2) and (3, 2).

3. Find the distance between (−2, −6) and (−2, 4).

4. A rectangle has vertices at (1, 1), (1, 5), (6, 5), and (6, 1). What is the perimeter?