Length of a Line (Cambridge International IGCSE Maths)

Length of a line

How do I calculate the length of a line?

• The distance between two points with coordinates (x_ 1 comma y_ 1) and (x_ 2 comma y_ 2) can be found using the formula

d=√((x_ 1−x_ 2)²+(y_ 1−y_ 2)²)

• This formula uses Pythagoras’ theorem $a^{2}+b^{2}=c^{2}$

  • It is applied to the difference in the $x$-coordinates and the difference in the $y$-coordinates

Exam Hint Be extra careful when negative coordinates are involved. It can help to put negative numbers in brackets to make your working clearer, e.g. (−6)−(−8)=2.

Worked Example Point A has coordinates (3, -4) and point B has coordinates (-5, 2).

Calculate the distance of the line segment AB.

Answer:

Using the formula for the distance between two points, d=√((x_ 1−x_ 2)²+(y_ 1−y_ 2)²)* *

Substitute in the two given coordinates

d=√((3−(−5))²+((−4)−2)²)

Be careful with the negative numbers 3−(−5)=8 and (−4)−2=−6

Simplify

d=√((8)²+(−6)²)=√(64+36)=√(100=10

Final answer: 10 units