1. The points (0,0), (0,5), (5,0) and (5,5) are the coordinates of a quadrilateral. a. Determine...

 

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1. The points (0,0), (0,5), (5,0) and (5,5) are the coordinates of a quadrilateral. a. Determine the shape of the quadrilateral. b. The quadrilateral is dilated with r=3, translated 2 units upward and 3 units toward the right, then rotated at 90 degrees clockwise. Determine the new coordinates of the quadrilateral. c. Graph the quadrilateral and its transformation. 2. Susan needs to mail a package at the post office, pick up several items at the grocery store, return a rented video, and make a deposit at her bank. The estimated driving time, in minutes, between each of these locations is given in the table below. Home Post office Grocery Video rental store Bank Home - 14 12 20 23 Post Office 14 - 8 12 21 Grocery 12 8 17 11 Video rental store 20 12 17 18 Bank 23 21 11 18 Use the greedy algorithm to design routes for Susan to follow that will help minimize her total driving time. Assume she must start from home and return home when her errands are done. 3. Represent the fictional map of countries below as a graph, and determine whether the graph is 2-colorable, 3-colorable, or 4-colorable by finding a suitable coloring of the graph. Then color the map according to the graph coloring. 4. Encrypt the statement "Success is not final; failure is not fatal: It is the courage to continue that counts." Using k=20. Decrypt the statement after encryption. 1. The points (0,0), (0,5), (5,0) and (5,5) are the coordinates of a quadrilateral. a. Determine the shape of the quadrilateral. b. The quadrilateral is dilated with r=3, translated 2 units upward and 3 units toward the right, then rotated at 90 degrees clockwise. Determine the new coordinates of the quadrilateral. c. Graph the quadrilateral and its transformation. 2. Susan needs to mail a package at the post office, pick up several items at the grocery store, return a rented video, and make a deposit at her bank. The estimated driving time, in minutes, between each of these locations is given in the table below. Home Post office Grocery Video rental store Bank Home - 14 12 20 23 Post Office 14 - 8 12 21 Grocery 12 8 17 11 Video rental store 20 12 17 18 Bank 23 21 11 18 Use the greedy algorithm to design routes for Susan to follow that will help minimize her total driving time. Assume she must start from home and return home when her errands are done. 3. Represent the fictional map of countries below as a graph, and determine whether the graph is 2-colorable, 3-colorable, or 4-colorable by finding a suitable coloring of the graph. Then color the map according to the graph coloring. 4. Encrypt the statement "Success is not final; failure is not fatal: It is the courage to continue that counts." Using k=20. Decrypt the statement after encryption.