Question

Find the distance between the following points: 

`(6 1/2, −3 3/4); (−2 1/2, 8 1/4)`

Answer 1

Let’s find the distance between the points:

`(6 1/2, −3 3/4) and (−2 1/2, 8 1/4)`

Step 1: Convert to improper fractions or decimals

`6 1/2 = 13/2, −3 3/4 = −15/4`

`−2 1/2 = − 5/2,  8 1/4 = 33/4`

`(13/2, −15/4) and (−5/2, 33/4)`

Step 2: 

`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

Substitute values:

= `sqrt((−5/2 − 13/2)^2 + (33/4 −(− 15/4))^2)`

= `sqrt((−18/2)^2 + ((33 + 15)/4)^2)`

= `sqrt((−9)^2 + (48/4)^2)`

= `sqrt(81 + 12^2)`

= `sqrt(81 + 144)`

= `sqrt225`

= 15 units