Question

she visited creepy cavern at (-2, 5), bernies 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?
sweet symphonies and bernies barn
whimsical wonders and rock and roll hall
creepy cavern and star gazing point
mystery mansion and whimsical wonders
bernies barn and mystery mansion
rock and roll hall and creepy cavern

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate distance for Sweet Symphonies (-3,-1) and Bernie's Barn (-3,2)

$x_1=-3,y_1 = - 1,x_2=-3,y_2 = 2$. Then $d=\sqrt{(-3+3)^2+(2 + 1)^2}=\sqrt{0 + 9}=3<6$.

Step3: Calculate distance for Whimsical Wonders (3,-4) and Rock and Roll Hall (2,-4)

$x_1=3,y_1=-4,x_2 = 2,y_2=-4$. Then $d=\sqrt{(2 - 3)^2+(-4 + 4)^2}=\sqrt{1+0}=1<6$.

Step4: Calculate distance for Creepy Cavern (-2,5) and Star Gazing Point (5,5)

$x_1=-2,y_1 = 5,x_2=5,y_2 = 5$. Then $d=\sqrt{(5 + 2)^2+(5 - 5)^2}=\sqrt{49+0}=7>6$.

Step5: Calculate distance for Mystery Mansion (3,2) and Whimsical Wonders (3,-4)

$x_1=3,y_1 = 2,x_2=3,y_2=-4$. Then $d=\sqrt{(3 - 3)^2+(-4 - 2)^2}=\sqrt{0 + 36}=6$.

Step6: Calculate distance for Bernie's Barn (-3,2) and Mystery Mansion (3,2)

$x_1=-3,y_1 = 2,x_2=3,y_2 = 2$. Then $d=\sqrt{(3 + 3)^2+(2 - 2)^2}=\sqrt{36+0}=6$.

Step7: Calculate distance for Rock and Roll Hall (2,-4) and Creepy Cavern (-2,5)

$x_1=2,y_1=-4,x_2=-2,y_2 = 5$. Then $d=\sqrt{(-2 - 2)^2+(5 + 4)^2}=\sqrt{16 + 81}=\sqrt{97}\approx9.85>6$.

Answer:

C. Creepy Cavern and Star Gazing Point
F. Rock and Roll Hall and Creepy Cavern