Exercise 38 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(1,3), into this formula and simplify.

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

Substitute ( 1,3) & ( -4,-2)

d=sqrt(( -4- 1)^2+( -2- 3)^2)

Subtract terms

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

Calculate power

d=sqrt(25+25)

Add terms

d=sqrt(50)

Use a calculator

d≈7.1

The distance between P and Q is PQ≈7.1.

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 ( 1,3) & ( -4,-2)

M(1+( -4)/2,3+( -2)/2)

a+(- b)=a-b

M(1-4/2,3-2/2)

Subtract terms

M(-3/2,1/2)

Divide by 2

M(-1.5,0.5)

The midpoint of PQ is the point (-1.5,0.5).

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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