Exercise 74 Page 402

Practice makes perfect

a Let's first plot AB and the three midpoints, C, D, and E.

To determine E we first have to find C. This will allow us to find D, which allows us to find E. We can find the midpoint of a segment with the Midpoint Formula.

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

SubstitutePoints

Substitute ( 14,10) & ( 2,2)

M_C(14+ 2/2,10+ 2/2)

▼

Simplify right-hand side

AddTerms

Add terms

M_C(16/2,12/2)

CalcQuot

Calculate quotient

M_C(8,6)

The midpoint of C is (8,6). Now we have enough information to find D.

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

SubstitutePoints

Substitute ( 8,6) & ( 2,2)

M_D(8+ 2/2,6+ 2/2)

▼

Simplify right-hand side

AddTerms

Add terms

M_D(10/2,8/2)

CalcQuot

Calculate quotient

M_D(5,4)

Finally, we have enough information to find E.

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

SubstitutePoints

Substitute ( 8,6) & ( 5,4)

M_E(8+ 5/2,6+ 4/2)

▼

Simplify right-hand side

AddTerms

Add terms

M_E(13/2,10/2)

CalcQuot

Calculate quotient

M_E(6.5,5)

The coordinates of E is (6.5,5).

b Let's label the distance between AC and BC as x.

This must mean that the distances AD and DC are both 0.5x.

Finally, the distances DE and EC are both 0.25x.

By adding the expressions for AD and DE and dividing by the distance of AB, we can get the fraction of the distance that E is from A to B.

0.5x+0.25x/0.5x+0.25x+0.25x+x

AddTerms

Add terms

0.75x/2x

ReduceFrac

a/b=.a /x./.b /x.

0.75/2

ExpandFrac

a/b=a * 4/b * 4

3/8

c By adding 38 of the vertical and horizontal distance between A and B to the x- and y-coordinates of A, we should end up at point E.

Let's add 38(12) to the x-coordinates of E and 38(8) to the y-coordinate of E. x_E:& 2+3/8(12) = 6.5 y_E:& 2 + 3/8(8) = 5 The coordinates of E is (6.5,5).