The map shows the location of a mall, library, and school in a city:Britney traveled from the school to the mall and then from the mall to the library. Alice traveled directly from the school to the library. How many more miles did Britney travel than Alice?A) 8 milesB) 9 milesC) 10 milesD) 12 miles

Accepted Solution

Answer:A) 8 miles.Step-by-step explanation:We  haven been given a map that shows the location of a mall, library, and school in a city.First of all we will find the distance traveled by Britney from school to mall and mall to library using distance formula.[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] Upon substituting the coordinates of school and mall in distance formula we will get,[tex]\text{Distance between school and mall}=\sqrt{(10-10)^2+(-4-6)^2}[/tex] [tex]\text{Distance between school and mall}=\sqrt{(0)^2+(-10)^2}[/tex] [tex]\text{Distance between school and mall}=\sqrt{0+100}[/tex] [tex]\text{Distance between school and mall}=10[/tex]  Now let us find distance between mall and library.[tex]\text{Distance between mall and library}=\sqrt{(10--14)^2+(6-6)^2}[/tex][tex]\text{Distance between mall and library}=\sqrt{(10+14)^2+(0)^2}[/tex][tex]\text{Distance between mall and library}=\sqrt{(24)^2+(0)^2}[/tex][tex]\text{Distance between mall and library}=\sqrt{576+0}[/tex][tex]\text{Distance between mall and library}=24[/tex][tex]\text{Total distance covered by Britney}=\text{10 miles +24 miles}[/tex][tex]\text{Total distance covered by Britney}=\text{34 miles}[/tex]Therefore, Britney traveled 34 miles.Now let us find the distance covered by Alice by substituting coordinates of school and library in distance formula.[tex]\text{Distance covered by Alice}=\sqrt{(10--14)^2+(-4-6)^2}[/tex] [tex]\text{Distance covered by Alice}=\sqrt{(10+14)^2+(-10)^2}[/tex] [tex]\text{Distance covered by Alice}=\sqrt{(24)^2+(-10)^2}[/tex] [tex]\text{Distance covered by Alice}=\sqrt{576+100}[/tex] [tex]\text{Distance covered by Alice}=\sqrt{676}[/tex] [tex]\text{Distance covered by Alice}=26[/tex] Therefore, Alice traveled 26 miles.[tex]\text{The number of miles Britney traveled more than Alice}=\text{34 miles -26 miles}[/tex][tex]\text{The number of miles Britney traveled more than Alice}=\text{8 miles}[/tex]Therefore, Britney traveled 8 miles more than Alice and option A is the correct choice.