Exercise 44 Page 54

Practice makes perfect

a PQ is the distance between the points P and Q. 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, P(4,2) and Q(3,0), into this formula and simplify.

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

Substitute ( 3,0) & ( 4,2)

d=sqrt(( 4- 3)^2+( 2- 0)^2)

Subtract terms

d=sqrt(1^2+2^2)

Calculate power

d=sqrt(1+4)

Add terms

d=sqrt(5)

Use a calculator

d≈2.2

The distance between P and Q is PQ≈2.2.

b Now we want to find the midpoint of the line segment PQ. 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 ( 3,0) & ( 4,2)

M(3+ 4/2,0+ 4/2)

Add terms

M(7/2,2/2)

Divide by 2

M(3.5,1)

The midpoint of PQ is the point (3.5,1).

Lesson Check p.53

Practice and Problem-Solving Exercises p.54-56

Standardized Test Prep p.56

Mixed Review p.56

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