Exercise 37 Page 401

Practice makes perfect

a Let's calculate the distance each player threw the ball.

Player A

Player A threw the ball to player B. We can calculate the length of the line segment between A and B using the Distance Formula.

Their coordinates are A(8,4) and B(18,7).

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

SubstitutePoints

Substitute ( 18,7) & ( 8,4)

AB = sqrt(( 18- 8)^2 + ( 7- 4)^2)

SubTerms

Subtract terms

AB=sqrt(10^2+3^2)

CalcPow

Calculate power

AB=sqrt(100+9)

AddTerms

Add terms

AB=sqrt(109)

UseCalc

Use a calculator

AB=10.44030...

RoundDec

Round to 1 decimal place(s)

AB≈10.4

Player A threw the ball approximately 10.4 meters.

Player B

Player B threw the ball to player C.

The length of the throw is the distance between B and C.

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

SubstitutePoints

Substitute ( 24,14) & ( 18,7)

BC = sqrt(( 24- 18)^2 + ( 14- 7)^2)

SubTerms

Subtract terms

BC=sqrt(6^2+7^2)

CalcPow

Calculate power

BC=sqrt(36+49)

AddTerms

Add terms

BC=sqrt(85)

UseCalc

Use a calculator

AB=9.21954...

RoundDec

Round to 1 decimal place(s)

AB≈9.2

Player B threw the ball around 9.2 meters.

b If player A would have thrown the ball directly to player C, the length of that throw would have been the distance between A and C.

We can use the Distance Formula, once again, to calculate the distance.

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

SubstitutePoints

Substitute ( 24,14) & ( 8,4)

AC = sqrt(( 24- 8)^2 + ( 14- 4)^2)

SubTerms

Subtract terms

AC=sqrt(16^2+10^2)

CalcPow

Calculate power

BC=sqrt(256+100)

AddTerms

Add terms

BC=sqrt(356)

UseCalc

Use a calculator

AC=18.86796...

RoundDec

Round to 1 decimal place(s)

AC≈18.9

Player A would have had to throw the ball around 18.9 meters.

Hints

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Practice exercises

Asses your skill

Player A

Player B