Exercise 39 Page 54

Practice makes perfect

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(-5,2) and Q(0,4), into this formula and simplify.

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

SubstitutePoints

Substitute ( 0,4) & ( -5,2)

d=sqrt(( -5- 0)^2+( 2- 4)^2)

SubTerms

Subtract terms

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

CalcPow

Calculate power

d=sqrt(25+4)

AddTerms

Add terms

d=sqrt(29)

UseCalc

Use a calculator

d≈5.4

The distance between P and Q is PQ≈5.4.

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 ( 0,4) & ( -5, 2)

M(0+( -5)/2,4+ 2/2)

AddNeg

a+(- b)=a-b

M(0-5/2,4+2/2)

AddSubTerms

Add and subtract terms

M(-5/2,6/2)

Div

Divide by 2