Question

She visited Creepy Cavern at (-2, 5), Bernie's Barn at (-3, 2), Sweet Symphonies at (-3, -1), Rock and Roll Hall at (-2, -4), Whimsical Wonders at (3, -4), Mystery Mansion at (3, 2), and Star Gazing Point at (5, 5). Which of these pairs of places are more than 6 units from one another?

Answer 1

First, plot each of the points and label them.

Determine the distance between the pairs of places listed in each answer choice.

Since Whimsical Wonders and Rock and Roll Hall lie on the same horizontal line, the distance between the two points is the absolute value of the difference of the x-coordinates.

Using this same process, the distance between Bernie's Barn and Mystery Mansion is 6 units, and the distance between Creepy Cavern and Star Gazing Point is 7 units.

Since the Mystery Mansion and Whimsical Wonders lie on the same vertical line, the distance between the two points is the absolute value of the difference of the y-coordinates.

Using this same process, the distance between Rock and Roll Hall and Creepy Cavern is 9 units, and the distance between Sweet Symphonies and Bernie's Barn is 3 units.

Therefore, the pairs of places that are more than 6 units from one another are Creepy Cavern and Star Gazing Point and Rock and Roll Hall and Creepy Cavern.

Explanation:

Answer 2

We need to find the distance between the pairs of points to know which is greater than 6units. To do that we make use of this formula:

`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Where
`(x_1 , y_1)` and
`(x_2 , y_2)` are two points on the line.

Let us denote Creepy Carven with CC, Bernie Barn as BB, Sweet Symphonies as SS, Rock and Roll Hall as RR, Whimsical Wonders as WW, Mysterial Mansion as MM and Star Grazing point as SG.

The distance between CC (-2, 5) and BB(-3, 2) using that formula will be:

`d = √((-3 + 2 )^2 + (2 - 5)^2)`

Which is
`d = √((-1 )^2 + (-3)^2)`

That gives

`d = √(10) < 6`

If we do this for BB to SS we have our value greater than 6, SS to RR our value greater than 6, RR to WW greater than 6, WW to MM is equal to 6 and MM to SG is less than 6.

From here we conclude that the pairs of places greater than 6 is:

BB to SS

SS to RR

RR to WW

WW to MM