Exercise 1 Page 585

Recall the Midpoint and the Distance Formulas.

Midpoint: M(-2,4)
Distance: about 7.2 units

Practice makes perfect

Let's find the coordinates of the midpoint and the distance one at a time.

Finding the Midpoint

To find the midpoint M, we can use the Midpoint Formula. M(x_1+x_2/2,y_1+y_2/2)The coordinates of the given endpoints are (-4,1) and (0,7). Let's use these to find the coordinates of the midpoint.

M(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( -4,1) & ( 0,7)

M(-4+ 0/2,1+ 7/2)

AddTerms

Add terms

M(-4/2,8/2)

CalcQuot

Calculate quotient

M(-2,4)

The midpoint is located at (-2,4).

Finding the Distance

To find the distance between the points, we can use the Distance Formula. d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) Let's substitute the given endpoints, P(-4,1) and Q(0,7), into this formula and simplify.

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

SubstitutePoints

Substitute ( -4,1) & ( 0,7)

d=sqrt(( 0-( -4))^2+( 7- 1)^2)

SubNeg

a-(- b)=a+b

d=sqrt(4^2+(7-1)^2)

SubTerm

Subtract term

d=sqrt(4^2+6^2)

CalcPow

Calculate power