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 Rico's 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 Spot Location (-4,3) (2,1) (1,3) (-4,1) (5,3) (-4,-2) (5,-1) 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.

Answer 1

Answer:

• See the graph attached an example below chosing three pairs or points.

Explanation:

I graphed the spots. Please, see the graph attached.

To calculate the distance between to points you use the distance formula:

      $distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Selecting some points, this is how you calculate the distance:

• (-4,3) and (5,3)

      $distance=\sqrt{(5-(-4))^2+(3-3)^2}=\sqrt{9^2}=9$

• (-4,3) and (5,-1)

      $distance=\sqrt{(5-(-4))^2+(3-(-1))^2}=\sqrt{9^2+4^2}=\sqrt{90}\approx9.5$

• (-4,-2) and (2,1)

       $distance=\sqrt{(2-(-4))^2+(1-(-2))^2}=\sqrt{6^2+3^2}=\sqrt{45}\approx6.7$

Thus, the order of the distances, for those pairs of points, ranked from longest to shortest are:

• AG > AB > BF