Question

she determined that the food court is at point (1, 1), the restrooms are at point (4, 3), the candy shop is at point (-6, 1), the gift shop is at point (-3, -3), the toy store is at point (-2, -2), the boutique is at point (7, 1), the hair salon is at point (-3, 3), and the electronics store is at point (4, -2). which of these pairs of places are 6 units from one another? the candy shop and the food court the food court and the boutique the toy store and the electronics store the electronics store and the restrooms the hair salon and the gift shop

Explanation:

Step1: Recall distance formula

The distance formula 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 between candy - shop $(-6,1)$ and food court $(1,1)$

Substitute $x_1=-6,y_1 = 1,x_2 = 1,y_2 = 1$ into the formula. $d=\sqrt{(1-(-6))^2+(1 - 1)^2}=\sqrt{(7)^2+0^2}=7$.

Step3: Calculate distance between food court $(1,1)$ and boutique $(7,1)$

Substitute $x_1 = 1,y_1=1,x_2 = 7,y_2 = 1$ into the formula. $d=\sqrt{(7 - 1)^2+(1 - 1)^2}=\sqrt{(6)^2+0^2}=6$.

Step4: Calculate distance between toy store $(-2,-2)$ and electronics store $(4,-2)$

Substitute $x_1=-2,y_1=-2,x_2 = 4,y_2=-2$ into the formula. $d=\sqrt{(4-(-2))^2+(-2+2)^2}=\sqrt{(6)^2+0^2}=6$.

Step5: Calculate distance between electronics store $(4,-2)$ and restrooms $(4,3)$

Substitute $x_1 = 4,y_1=-2,x_2 = 4,y_2 = 3$ into the formula. $d=\sqrt{(4 - 4)^2+(3+2)^2}=\sqrt{0+(5)^2}=5$.

Step6: Calculate distance between hair salon $(-3,3)$ and gift shop $(-3,-3)$

Substitute $x_1=-3,y_1 = 3,x_2=-3,y_2=-3$ into the formula. $d=\sqrt{(-3+3)^2+(-3 - 3)^2}=\sqrt{0+( - 6)^2}=6$.

Answer:

B. the food court and the boutique
C. the toy store and the electronics store
E. the hair salon and the gift shop