Length of a Line Flashcards

All 6 cards in this deck

What is the formula for the length of the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$?

$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ (Pythagoras' theorem)

What are the steps to find the length of a line segment from its endpoints?

e.g. $A(1, 2)$ and $B(4, 6)$

1. Differences: $4-1 = 3$ and $6-2 = 4$
2. Square and add: $3^2 + 4^2 = 25$
3. Square root: $\sqrt{25} = 5$

True or false? It does not matter which point you subtract from which when finding the length of a line segment.

True. The differences are squared, so the sign makes no difference.

True or false? The horizontal distance between two points with $x$-coordinates $-7$ and $8$ is $1$.

False. It is $8 - (-7) = 15$.

What can you work out to prove that a triangle on coordinate axes is isosceles?

The length of each side using Pythagoras, then show two lengths are equal.

True or false? Showing that two sides of a quadrilateral on coordinate axes have equal length proves it is a rhombus.

False. You must show all four sides have equal length.