Exercise 38 Page 402

To model this situation, we can use a coordinate plane where the different axes represent different cardinal directions (north, south, east, and west). If we place your house at the origin and let each unit represent a block, the school is placed at S(20,-12).

To find the distance between the school and the mall, we can calculate the length of the line segment SM.

Let's use the Distance Formula to find the distance.

SM = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( -7,10) & ( 20,-12)

SM = sqrt(( -7- 20)^2 + ( 10-( -12))^2)

SubTerm

Subtract term

SM=sqrt((-27)^2+(10-(-12))^2)

SubNeg

a-(- b)=a+b

SM=sqrt((-27)^2+22^2)

UseCalc

Use a calculator

SM=34.82814...

RoundDec

Round to 1 decimal place(s)

SM≈34.8

The distance between the mall and the school is about 34.8 blocks. Since each block is 0.1 mile, we can multiply by this conversion factor to find the distance in miles. 34.8* 0.1=3.48≈ 3.5 miles