Question

(1) (7 total points)

Line segment AB has endpoints A(-2, 0) and B(4, 8).
Point C is on the line segment AB and is located at (2.5, 6).
What is the ratio of CB
AC
? DO NOT use the Section Formula to solve this problem.

Show me: (show all math work needed to calculate each part)
a) graph of segment AB with points A, B, C labeled and showing (x, y) coordinates (3 points)
b) length of segment AC (1 point)
c) length of segment CB (1 point)
d) ratio CB
AC
(1 point)
e) reduced fraction CB
AC
(1 point)

Answer 1

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

3AC=CB

CB

AC

=

3

1

Since, A(1,1) and B(2,3) & m:n=1:3

Therefore, we have

C(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

(

1+3

(1)(2)+3(1)

,

1+3

(1)(3)+3(1)

)

C→(

4

5

,

2

3

).

Explanation: