Exercise 8 Page 539

Practice makes perfect

a To find the midpoint between your house and your friend's we can use the Midpoint Formula. From the coordinate plane, we see that your house is at (3,2) and the friend's house is at (3,8).

M(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( 3,2) & ( 3,6)

M(3+ 3/2,2+ 8/2)

▼

Simplify

AddTerms

Add terms

M(6/2,10/2)

CalcQuot

Calculate quotient

M(3,5)

The midpoint is at (3,5).

b Both you and your friend first walks to the meeting point at (3,5).

Next, we have to determine the distance from the meeting point to the school. From the coordinate plane, we see that the segment between the meeting point and the school is between (3,5) and (8,6).

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

SubstitutePoints

Substitute ( 8,6) & ( 3,5)

d=sqrt(( 8- 3)^2+( 6- 5)^2)

SubTerms

Subtract terms

d=sqrt(5^2+1^2)

CalcPow

Calculate power

d=sqrt(25+1)

AddTerms

Add terms

d=sqrt(26)

The distance from the meeting point to the school is sqrt(26). By adding the distances you or your friend has to walk to get to school, and multiply by 50, we get the total distance in yards: 50(sqrt(26)+3)≈ 405 yards.

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Exercises p.538-539

Exercise 8 Page 539

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