Coordinate Plane (1st Quadrant) • Topic 3 of 3

Horizontal & Vertical Distance Between Points

Finding Distance on a Coordinate Plane

Since we're only in the first quadrant, all coordinates are positive. Distances are always positive.

Horizontal Distance (Left to Right):

Points have the same y-coordinate
Distance = |x₂ - x₁|

Vertical Distance (Up and Down):

Points have the same x-coordinate
Distance = |y₂ - y₁|

Distance Formula for Same Row/Column:

Horizontal: |x₂ - x₁|
Vertical:   |y₂ - y₁|

Note: | | means "absolute value" (always positive)

HORIZONTAL DISTANCE (Same y):

    y=5   A(2,5)     B(7,5)
           • ←─ 5 units ─→ •
           
    Distance = |7 - 2| = 5 units
    
    <---|---|---|---|---|--->
    2   3   4   5   6   7


VERTICAL DISTANCE (Same x):

    y=8           B(4,8)
                  •
                  ↑
                  │ 3 units
                  ↓
    y=5   A(4,5)
           •
           
    Distance = |8 - 5| = 3 units


BOTH HORIZONTAL & VERTICAL (L-shaped path):

    y=7          B(9,7)
                  •
                  ↑
                  │ 4 units
                  ↓
    y=3   A(3,3)  •
           ← 6 units →  C(9,3)
                        •
    
    Horizontal distance = 6 units
    Vertical distance = 4 units
    Total path (taxicab distance) = 6 + 4 = 10 units


FINDING DISTANCE - STEP BY STEP:

    Points: P(2,8) and Q(2,3)
    
    Step 1: Same x? YES (both x=2)
    Step 2: Distance = |8 - 3| = 5 units
    
    Points: R(1,4) and S(6,4)
    
    Step 1: Same y? YES (both y=4)
    Step 2: Distance = |6 - 1| = 5 units

Solved Examples

Worked Example

Find the distance between A(3, 5) and B(8, 5).

Solution

Same y-coordinate (y=5) → horizontal distance
Distance = |8 - 3| = 5
Answer: 5 units

Worked Example

Find the distance between C(2, 1) and D(2, 9).

Solution

Same x-coordinate (x=2) → vertical distance
Distance = |9 - 1| = 8
Answer: 8 units

Worked Example

A bird is at (4, 6) and its nest is at (4, 2). How far must it fly straight down?

Solution

Same x (both 4) → vertical
Distance = |6 - 2| = 4
Answer: 4 units

Worked Example

Two points: (5, 3) and (12, 3). What is the horizontal distance?

Solution

Same y=3
Distance = |12 - 5| = 7
Answer: 7 units

Key Points

Same x → vertical distance (|y₂ - y₁|)
Same y → horizontal distance (|x₂ - x₁|)
Distance is always positive
Units depend on grid scale
To find L-shaped path: add horizontal + vertical

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Two points with the same $y$-coordinate lie on a:

Explanation: Horizontal line.

Q2.Two points with the same $x$-coordinate lie on a:

Explanation: Vertical line.

Q3.The distance between $(1,2)$ and $(5,2)$ is:

Explanation: $5-1=4$.

Q4.Distance is always:

Explanation: Positive.

Practice more MCQs → 📝 Assignment · 35 marks