Coordinate Plane (4 Quadrants) • Topic 2 of 2

Finding Distance Between Points on Horizontal/Vertical Lines

Finding Distance on a Coordinate Plane

When points share the same x-coordinate (vertical line) or same y-coordinate (horizontal line), distance is easy to find!

Horizontal Distance (same y-coordinate):

Distance = |x₂ - x₁|
Points move left or right only

Vertical Distance (same x-coordinate):

Distance = |y₂ - y₁|
Points move up or down only

Important: Distance is always positive (absolute value)

HORIZONTAL DISTANCE (Same y):

    Points: A(-3, 2) and B(4, 2)
    
    y=2 ──────────────────────────
         ●           ●
        A(-3,2)     B(4,2)
    
    Distance = |4 - (-3)| = |4 + 3| = 7 units
    
    <───────── 7 units ─────────>


VERTICAL DISTANCE (Same x):

    Points: C(2, 5) and D(2, -3)
    
         ● C(2,5)
         │
         │
         │ 8 units
         │
         │
         ● D(2,-3)
    
    Distance = |5 - (-3)| = |5 + 3| = 8 units


BOTH DIRECTIONS (L-shaped path):

    From E(-2, 3) to F(4, -2)
    
    Step 1 (horizontal): from (-2,3) to (4,3)
    Distance = |4 - (-2)| = 6 units
    
    Step 2 (vertical): from (4,3) to (4,-2)
    Distance = |3 - (-2)| = 5 units
    
    Total L-shaped path = 6 + 5 = 11 units


IDENTIFYING HORIZONTAL/VERTICAL LINES:

    Horizontal line: y-coordinates are the SAME
    Vertical line:   x-coordinates are the SAME
    
    Check: (3,5) and (8,5) → same y=5 → horizontal!
    Check: (-2,4) and (-2,-7) → same x=-2 → vertical!

Solved Examples

Worked Example

Find the distance between A(-4, 3) and B(6, 3)

Solution

Same y = 3 → horizontal distance
Distance = |6 - (-4)| = |6 + 4| = 10
Answer: 10 units

Worked Example

Find the distance between C(2, 5) and D(2, -7)

Solution

Same x = 2 → vertical distance
Distance = |5 - (-7)| = |5 + 7| = 12
Answer: 12 units

Worked Example

Find the distance between E(-5, -2) and F(3, -2)

Solution

Same y = -2 → horizontal distance
Distance = |3 - (-5)| = |3 + 5| = 8
Answer: 8 units

Worked Example

Point P is at (-3, 4). Point Q is at (-3, -5). What is the distance?

Solution

Same x = -3 → vertical distance
Distance = |4 - (-5)| = |4 + 5| = 9
Answer: 9 units

Key Points

Same y → horizontal line → subtract x-coordinates
Same x → vertical line → subtract y-coordinates
Use absolute value for positive distance
Count units on the grid to verify
Distance formula for diagonal points will come later

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