Exercise 42 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,-5) and Q(-1,1), into this formula and simplify.

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

SubstitutePoints

Substitute ( -1,1) & ( -4,-5)

d=sqrt(( -4-( -1))^2+( -5- 1)^2)

SubNeg

a-(- b)=a+b

d=sqrt((-4+1)^2+(-5-1)^2)

AddSubTerms

Add and subtract terms

d=sqrt((-3)^2+(-6)^2)

CalcPow

Calculate power

d=sqrt(9+36)

AddTerms

Add terms

d=sqrt(45)

UseCalc

Use a calculator

d≈6.7

The distance between P and Q is PQ≈6.7.

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)

SubstitutePoints

Substitute ( -1,1) & ( -4,-5)

M(-1+( -4)/2,1+( -5)/2)

AddNeg

a+(- b)=a-b

M(-1-4/2,1-5/2)

SubTerms

Subtract terms

M(-5/2,-4/2)

Div

Divide by 2

M(-2.5,-2)

The midpoint of PQ is the point (-2.5, -2).

Subchapter links

Lesson Check p.53

Practice and Problem-Solving Exercises p.54-56

Standardized Test Prep p.56

Mixed Review p.56

Exercise 42 Page 54

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