Question

Layana’s house is located at (2 and two-thirds, 7 and one-third) on a map. The store where she works is located at (–1 and one-third, 7 and one-third). What is the distance from Layana’s home to the store?

Answer 1

the distance from Layana’s home to the store is 4 units .

Step-by-step explanation:

We know that distance between two points
`P(x_1,y_1),Q(x_2,y_2)` is given by :

⇒
`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

According to question we have ,

`P(x_1,y_1 )= (2(2)/(3), 7(1)/(3)) = ((8)/(3),(22)/(3))\\Q(x_2,y_2) =( -1(1)/(3), 7(1)/(3)) = ( -(4)/(3), (22)/(3))`

Putting these values in above equation we get :

⇒
`D = \sqrt{(-(4)/(3)-(8)/(3))^2+((22)/(3)-(22)/(3))^2}`

⇒
`D = \sqrt{(-(12)/(3))^2}`

⇒
`D =(12)/(3)`

⇒
`D =4`

Therefore , the distance from Layana’s home to the store is 4 units .

Answer 2

The distance between Layana's house and store is 4 units.

Step-by-step explanation:

Given:

Coordinates of Layana's house =
`(2(2)/(3) , 7(1)/(3))`

Coordinates of the store =
`(-1(1)/(3), 7(1)/(3))`

It can also be written as:

Coordinates of Layana's house =
`((8)/(3) , (22)/(3))`

Coordinates of the store =
`(-(4)/(3), (22)/(3))`

The distance between the house and the shop is:

`d = √((x_2-x_1)^2 + (y_2-y_1)^2)`

On substituting the value we get:

`d = \sqrt{((-4 - 8)/(3) )^2 + ((22-22)/(3) )^2} \\\\d = \sqrt{(144)/(9) } \\\\d = (12)/(3) \\\\d = 4 units`

Therefore, the distance between Layana's house and store is 4 units.