Exercise 21 Page 404

We can begin the solution by mapping the outlines of the baseball field as points in a diagram. We can write the relative positions as coordinates and also enter the given distances. We will call home plate H, the pitching mound P, and the bases F, S, and T.

We can now make use of the knowledge that the distance from home plate to first base is 90 ft. Let's rewrite the coordinates for first base as (90,0). From the relative positions, we also know that home plate and the three bases form a square. We can use this knowledge to rewrite the other coordinates as well.

Now that we've rewritten the coordinates, all of the measurements are in feet. We can now use the Distance Formula to calculate the distances.

Distance from home plate to second base

We will use the coordinates H(0,0) and S(90,90) to calculate the distance from home plate to second base.

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

SubstitutePoints

Substitute ( 90,90) & ( 0,0)

HS = sqrt(( 90- 0)^2 + ( 90- 0)^2)

SubTerms

Subtract terms

HS=sqrt(90^2+90^2)

UseCalc

Use a calculator

HS=127.27922 ...

RoundDec

Round to 1 decimal place(s)

HS ≈ 127.3

The distance from the home base to the second base is approximately 127.3 ft.

Distance from home plate to pitching mound

We can now calculate the distance from the home plate to the pitching mound. We will use the Distance Formula and the points H(0,0) and P(45,45).

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

SubstitutePoints

Substitute ( 45,45) & ( 0,0)

HP = sqrt(( 45- 0)^2 + ( 45- 0)^2)

SubTerms

Subtract terms

HP=sqrt(45^2+45^2)

UseCalc

Use a calculator

HP=63.63961 ...

RoundDec

Round to 1 decimal place(s)

HP ≈ 63.6

The distance from the home base to the pitching mound is approximately 63.6 ft.