Exercise 52 Page 224

To determine the distance between two points, we use the Distance Formula. The coordinates of the given points are A(2,-6) and B(-3,6).

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

SubstitutePoints

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

AB=sqrt(( -3- 2)^2+( 6-( -6))^2)

SubNeg

a-(- b)=a+b

AB=sqrt((-3-2)^2+(6+6)^2)

AddSubTerms

Add and subtract terms

AB=sqrt((-5)^2+12^2)

CalcPow

Calculate power

AB=sqrt(25+144)

AddTerms

Add terms

AB=sqrt(169)

CalcRoot

Calculate root

AB=13

The distance between point A and point B is 13.