Distance Formula

Find the shortest distance between each of the following pairs of points.
Show your working and round your answers to the nearest tenth.

1

(–1, 4) and (3, 10)

1

(–7, –11) and (4, –25)

1

When data is sent electronically, for example when you download a song, you don’t want parts of it to be missing. Computer programmers, who imagine data as points in space, use Pythagoras’ theorem to make sure that the data is where it should be.
Given an original point and its nal location, determine whether or not a piece of data is where it should be (a distance d from its original location). Copy and complete this table.

In video games, the location of each character is tracked using coordinates. The program uses Pythagoras’ theorem to calculate the distance between characters.
It then compares this value with minimum distances that have been set for certain actions. For example, a role-playing game is programed to register a “hit” by a character’s sword if the character is within 2 units of her opponent.

1

In which of the following scenarios would a “hit” be registered?

1

(–1, 4) and (3, 10)

(–7, –11) and (4, –25)

In which of the following scenarios would a “hit” be registered?

Establish a location for two players (other than those above) where a “hit” would beregistered. Justify your answer.

Establish a location for two players (other than those above) where a “hit” would be
registered. Justify your answer.