Exercise 64 Page 67

Practice makes perfect

a AB is the distance between the points A and B. 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, A(4,1) and B(7,9), into this formula and simplify.

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

Substitute ( 7,9) & ( 4,1)

d = sqrt(( 7- 4)^2 + ( 9- 1)^2)

Subtract terms

d=sqrt((3)^2+(8)^2)

Calculate power

d=sqrt(9+64)

Add terms

d=sqrt(73)

Use a calculator

d=8.5440...

Round to 1 decimal place(s)

d≈8.5

The distance between A and B is AB≈8.5.

b Now we want to find the midpoint of the line segment AB. We can use the Midpoint Formula.

M ( x_1+x_22, y_1+y_22) Let's substitute the coordinates into this formula.

M(x_1+x_2/2,y_1+y_2/2)

Substitute ( 4,1) & ( 7,9)

M(4+ 7/2,1+ 9/2)

Add terms

M(11/2,10/2)

Divide by 2

M(5.5,5)

The midpoint of AB is the point (5.5, 5).

Lesson Check p.64

Practice and Problem-Solving Exercises p.64-67

Standardized Test Prep p.67

Mixed Review p.67

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