Question

the four corners of a rectangular city block are located at (-5, -2), (-5, 9), (9, 9), and (9, -2) on the coordinate grid below. randy walks all the way around the block and stops when he gets back to where he started. each unit on the grid represents 10 meters. how many meters does randy walk? type the answer in the box below.

Explanation:

Step1: Calculate the length of one - side

The length of the horizontal side of the rectangle can be found by calculating the difference in the x - coordinates of two adjacent vertices. Let's take two adjacent vertices \((- 5,-2)\) and \((9,-2)\). The length of the horizontal side \(l_{1}=\vert9 - (-5)\vert=\vert9 + 5\vert = 14\) units. Since each unit represents 10 meters, the length of this side in meters is \(14\times10=140\) meters.

Step2: Calculate the length of the other side

Take two adjacent vertices \((-5,-2)\) and \((-5,9)\). The length of the vertical side \(l_{2}=\vert9-(-2)\vert=\vert9 + 2\vert=11\) units. Since each unit represents 10 meters, the length of this side in meters is \(11\times10 = 110\) meters.

Step3: Calculate the perimeter

The perimeter \(P\) of a rectangle is given by \(P = 2(l_{1}+l_{2})\). Substitute \(l_{1}=140\) meters and \(l_{2}=110\) meters into the formula: \(P=2(140 + 110)=2\times250=500\) meters.

Answer:

500