Question

nick has located several digging spots that his dog, rico, has made in the backyard. to remember where all the spots were, nick plotted the points on a coordinate grid so he could fill the digging spots up later. on his coordinate grid drawing, the length of each square is one yard. nick placed ricos dog house at the origin and then plotted the digging spots based on the information table below.

spot labels	a	b	c	d	e	f	g

nick is looking at the coordinate grid to determine the distance between some of the digging spots. place the tiles in order from longest distance to shortest distance.
distance between spot a and spot c
distance between spot a and spot d
distance between spot e and spot g
distance between spot d and spot f
distance between spot b and spot d

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 spot A(-4,3) and spot C(1,3)

Substitute $x_1=-4,y_1 = 3,x_2=1,y_2 = 3$ into the formula: $d_{AC}=\sqrt{(1-(-4))^2+(3 - 3)^2}=\sqrt{(1 + 4)^2+0^2}=\sqrt{25}=5$.

Step3: Calculate distance between spot A(-4,3) and spot D(-4,1)

Substitute $x_1=-4,y_1 = 3,x_2=-4,y_2 = 1$ into the formula: $d_{AD}=\sqrt{(-4-(-4))^2+(1 - 3)^2}=\sqrt{0^2+(-2)^2}=2$.

Step4: Calculate distance between spot E(5,3) and spot G(5,-1)

Substitute $x_1=5,y_1 = 3,x_2=5,y_2=-1$ into the formula: $d_{EG}=\sqrt{(5 - 5)^2+(-1 - 3)^2}=\sqrt{0^2+(-4)^2}=4$.

Step5: Calculate distance between spot D(-4,1) and spot F(-4,-2)

Substitute $x_1=-4,y_1 = 1,x_2=-4,y_2=-2$ into the formula: $d_{DF}=\sqrt{(-4-(-4))^2+(-2 - 1)^2}=\sqrt{0^2+(-3)^2}=3$.

Step6: Calculate distance between spot B(2,1) and spot D(-4,1)

Substitute $x_1=2,y_1 = 1,x_2=-4,y_2 = 1$ into the formula: $d_{BD}=\sqrt{(-4 - 2)^2+(1 - 1)^2}=\sqrt{(-6)^2+0^2}=6$.

Step7: Order distances from longest to shortest

The distances are $d_{BD}=6$, $d_{AC}=5$, $d_{EG}=4$, $d_{DF}=3$, $d_{AD}=2$.

Answer:

distance between spot B and spot D, distance between spot A and spot C, distance between spot E and spot G, distance between spot D and spot F, distance between spot A and spot D