Exercise 37 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(0,-2) and Q(3,3), into this formula and simplify.

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

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

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

Subtract terms

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

Calculate power

d=sqrt(9+25)

Add terms

d=sqrt(34)

Use a calculator

d≈5.8

The distance between P and Q is PQ≈5.8.

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 ( 3,3) & ( 0,-2)

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

a+(- b)=a-b

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

Add and 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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