Question

your school is 4 miles east and 1 mile south of your apartment. a recycling center, where your class is going on a field trip, is 2 miles east and 3 miles north of your apartment. estimate the distance between the recycling center and your school.
round to the nearest tenth.
miles
a park is 3 miles east and 4 miles south of your apartment. find the distance between the park and your school.
round to the nearest tenth.
miles

Explanation:

Step1: Assign coordinates to locations

Let apartment = $(0,0)$.
School: $(4, -1)$ (4 east, 1 south)
Recycling center: $(2, 3)$ (2 east, 3 north)
Park: $(3, -4)$ (3 east, 4 south)

Step2: Distance formula for recycling center & school

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Substitute values: $d_1=\sqrt{(4-2)^2+(-1-3)^2}$

Step3: Calculate recycling center-school distance

$d_1=\sqrt{(2)^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}\approx4.5$

Step4: Distance formula for park & school

Substitute values: $d_2=\sqrt{(4-3)^2+(-1-(-4))^2}$

Step5: Calculate park-school distance

$d_2=\sqrt{(1)^2+(3)^2}=\sqrt{1+9}=\sqrt{10}\approx3.2$

Answer:

Distance between recycling center and school: 4.5 miles
Distance between park and school: 3.2 miles