Exercise 65 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(0,3) and B(-3,8), into this formula and simplify.

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

Substitute ( -3,8) & ( 0,3)

d = sqrt(( -3- 0)^2 + ( 8- 3)^2)

Subtract terms

d=sqrt((-3)^2+(5)^2)

Calculate power

d=sqrt(9+25)

Add and subtract terms

d=sqrt(34)

Use a calculator

d≈5.8

The distance between A and B is AB≈5.8.

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 ( -3,8) & ( 0,3)

M(0+( -3)/2,3+ 8/2)

a+(- b)=a-b

M(0-3/2,3+8/2)

Add terms

M(-3/2,11/2)

Divide by 2

M(-1.5,5.5)

The midpoint of AB is the point (-1.5, 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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