Exercise 46 Page 590

To determine the distance between two points, we use the Distance Formula. The coordinates of the given points are E(- 3,- 2) and F(5,8).

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

SubstitutePoints

Substitute ( - 3,- 2) & ( 5,8)

EF=sqrt(( 5-( - 3))^2+( 8-( - 2))^2)

SubNeg

a-(- b)=a+b

EF=sqrt((5+3)^2+(8+2)^2)

AddTerms

Add terms

EF=sqrt(8^2+10^2)

CalcPow

Calculate power

EF=sqrt(64+100)

AddTerms

Add terms

EF=sqrt(164)

CalcRoot

Calculate root

EF ≈ 12.8

The distance between E and F is approximately 12.8.