Exercise 16 Page 404

Use the Midpoint Formula and the Distance Formula.

Midpoint Coordinates: M(1/2,1)
Distance: sqrt(145)≈12

Practice makes perfect

We are asked to calculate the midpoint of two points and the distance between them. Let's do each step separately.

Calculating the Midpoint

To find the midpoint, we can use the Midpoint Formula. (x_1+x_2/2,y_1+y_2/2)The coordinates of the given endpoints are (-4,5) and (5,-3). Let's use these to find the coordinates of the midpoint.

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

SubstitutePoints

Substitute ( -4,5) & ( 5,-3)

M(-4+ 5/2,5+( -3)/2)

AddNeg

a+(- b)=a-b

M(-4+5/2,5-3/2)

AddSubTerms

Add and subtract terms

M(1/2,2/2)

QuotOne

a/a=1

M(1/2,1)

The midpoint is located at ( 12,1). We can see that on the graph.

Calculating the Distance

To determine the distance between two points, we can use the Distance Formula. Recall that the coordinates of the given points are L(-4,5) and N(5,-3).

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

SubstitutePoints

Substitute ( -4,5) & ( 5,-3)

LN=sqrt(( 5-( -4))^2+( -3- 5)^2)

SubNeg

a-(- b)=a+b

LN=sqrt((5+4)^2+(-3-5)^2)

AddSubTerms

Add and subtract terms

LN=sqrt(9^2+(-8)^2)

CalcPow

Calculate power