A segment with endpoints A (3, 4) and C (5, 11) is partitioned by a point B such that AB and BC form a 2:3 ratio. Find B. (3.8, 6.8)
(3.9, 4.8)
(4.2, 5.6)
(4.3, 5.9)

(3.8, 6.8)

Step-by-step explanation:

Point B:

Has coordinates (x,y)

AB and BC form a 2:3 ratio.

This means that:

We apply this both for the x-coordinate and for the y-coordinate.

x-coordinate:

x-coordinate of A: 3

x-coordinate of C: 5

x-coordinate of B: x

y-coordinate:

y-coordinate of A: 4

y-coordinate of C: 11

y-coordinate of B: y

Thus the correct answer is:

(3.8, 6.8)

true

explanation:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2