Given: A grocery store is located at the origin (0,0). Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store.
Required: To determine the coordinates of Madison's house and Gavin's house and the distance between the grocery store and madison's and Gavin's house. Also, write inequalities for the distance.
Step-by-step explanation: Let the graph represents the directions as follows-
Then, the direction west lies on the negative x-axis. So, according to the question, Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store. This can be represented as follows-
Here, M represents Madison's house, and G represents Gavin's house. Now the distance from the grocery store to Madison's house is 3 blocks and to Gavin's house is 5 blocks.
Gavin lives at a greater distance from the store. Let d(M) represent the distance of Madison's house from the store and d(G) represent the distance of Gavin's house from the store. Then-
![\begin{gathered} 0<strong>Final Answer: Coordinates of Madison's house=(0,-3).</strong><p><strong>Coordinate of Gavin's house=(0,-5)</strong></p><p><strong>Distance from the grocery store to Madison's house=3 unit blocks.</strong></p><p><strong>Distance from the grocery store to Gavin's house=5 unit blocks.</strong></p><p><strong>Inequalities are-</strong></p>[tex]\begin{gathered} 0\lt d(M))\leqslant3 \\ 0\lt d(G))\leqslant5 \end{gathered}]()