Exercise 62 Page 511

We want to find the distance between the points (4,2) and (2,- 5). To find this distance, we can use the Distance Formula. d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) Let's substitute the given coordinates, (4,2) and (2,- 5), into this formula and simplify.

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

SubstitutePoints

Substitute ( 4,2) & ( 2,- 5)

d=sqrt(( 2- 4)^2+( - 5- 2)^2)

SubTerms

Subtract terms

d=sqrt((- 2)^2+(- 7)^2)

CalcPow

Calculate power

d=sqrt(4+49)

AddTerms

Add terms

d=sqrt(53)

The distance between the points is sqrt(53).