Question

question 5 2020 geometry module2
zines is using a coordinate grid to map out how far she biked from each place in town.
if each unit on the grid represents 1 kilometer. zines traveled km. round to the nearest kilometer, if necessar

Explanation:

Step1: Find the length of \( MN \)

The coordinates of \( M(-4,2) \) and \( N(2,2) \).
Using the distance formula for horizontal line \( d=\vert x_2 - x_1\vert \), \( d=\vert2-(-4)\vert=\vert2 + 4\vert = 6\)

Step2: Find the length of \( MP \)

The coordinates of \( M(-4,2) \) and \( P(-2,6) \).
Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), \(d=\sqrt{(-2+4)^2+(6 - 2)^2}=\sqrt{2^2+4^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.47\)

Step3: Find the length of \( NP \)

The coordinates of \( N(2,2) \) and \( P(-2,6) \).
Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), \(d=\sqrt{(-2 - 2)^2+(6 - 2)^2}=\sqrt{(-4)^2+4^2}=\sqrt{16+16}=\sqrt{32}\approx5.66\)

Step4: Calculate the total distance

The total distance \( D=MN+MP+NP\), \(D = 6+4.47+5.66=16.13\approx16\)

Answer:

\(16\)