Question

Item 16 Question 1 There are three hallways at Wilson Middle School, as represented in the coordinate plane below. Four points are plotted on the coordinate plane to represent the end of each hallway. Clockwise from the top left, the points reed, A, negative 20, 60, D, 50, 75, C, 50, negative 25, B, negative 20, negative 25. Part A Each unit represents 1 meter. What is the total length of the three hallways? Show or explain your work.

please answer this question because i really don't know this

Answer 1

The total length of the three hallways is 241.59 meter.

Explanation:

Since we need to count the hallways in clockwise direction, We need to find the distance between A(-20, 60) and D(50, 75), D(50, 75) and C(50, -25), C(50, -25) and B(-20, -25).

Then we need to add the three of them.

Hence all we need to do is to find the difference between the respective points.

The length of the hallway AD is =
`\sqrt{[(50 + 20)^(2) + (75 - 60)^(2)  ]} = \sqrt{(70^(2) + 15^(2) )} = √(5125)` ≅ 71.59

Similarly, for DC is =
`\sqrt{[(50 - 50)^(2) + (75 + 25)^(2)  ]} = \sqrt{100^(2) } = <strong>100</strong>` and CB is =
`\sqrt{[(50 + 20)^(2) + (- 25 + 25)^(2)  ]} = \sqrt{70^(2) + 0} = <strong>70</strong>`

Hence, the total length of the hallways is
`70 + 100 + 71.59 = <strong>241.59</strong>`