Find the Distance on a Line between 2 Coordinates
Distance = √(y1 - y2)2 + (x1 - x2)2
Example
(a) What is the distance between p and q?
(b) What is the gradient of the line?
(c) What is the equation of the line?
(a) What is the distance between p and q?
Let's also see how the formula is derived.
Distance = √(y1 - y2)2 + (x1 - x2)2
Using Pythagoras Theorem to find the distance.
c2 = a2 + b2
Step 1 : Find the Coordinate for k(x,y) => to get a and b
Mark p and q coordinates on x and y axes.
a = 5 - 1 = 4
b= 6 - 3 = 3
Step 2 : Use c2 = a2 + b2 to find L
L2 = 32 + 42
= 9 + 16
L2 = 25
L = √25
= 5
(b) What is the gradient of the line?
Gradient = y2 - y1 (Step 1 : Write Formula)
x2 - x1
= 6 - 3 / 5 - 1. (Step 2 : substr and calculate)
= 3/4
(c) What is the equation of the line?
Equation of the line y = mx + c
Step 1 : What is lacking in the equation? c (y intercept)
Identify values to find c : m = gradient = 3/4 and (x,y) = (1,3)
Substitute values into the equation:
3 = 3/4(1) + c
c = 3 - 3/4 = 2 1/4
Step 2 : Form the Equation
Equation of the line : y=3/4x + 2 1/4
Example
Find the distance between (-7, -1), (5,4).
L = Distance = √(y1 - y2)2 + (x1 - x2)2 (Step 1 : Write Formula)
L = √( -7 -5)2 + (-1 - 4)2 (Step 2 : Substr value)
= √144 + 25
= √169
= 1
