Exercise 51 Page 508

To determine the distance between two points, we use the Distance Formula. The coordinates of the given points are R(- 6,10) and S(8,- 2).

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

SubstitutePoints

Substitute ( - 6,10) & ( 8,- 2)

RS=sqrt(( 8-( - 6))^2+( - 2- 10)^2)

SubNeg

a-(- b)=a+b

RS=sqrt((8+6)^2+(- 2-10)^2)

AddSubTerms

Add and subtract terms

RS=sqrt(14^2+(- 12)^2)

CalcPow

Calculate power

RS=sqrt(196+144)

AddTerms

Add terms

RS=sqrt(340)

CalcRoot

Calculate root

RS ≈ 18.4

The distance between R and S is approximately 18.4.