A segment with endpoints A (2, 6) and C (5,9) is partitioned by a point B such that AB
and BC form a 3:1 ratio. Find B. (5 points)
A.) (3.66, 7.66)
B.) (4.25, 8.25)
C.) (3.5, 10.5)
D.) (2.33, 6.33)

In geometry, points are used to divide segments into subsegments using partitions or ratios. The location of B is: (4.25,8.25)

The given parameters are:

[tex]A = (2,6)[/tex] -- [tex](x_1,y_1)[/tex]

[tex]C =(5,9)[/tex] -- [tex](x_2,y_2)[/tex]

[tex]m:n = 3 : 1[/tex]

To calculate the B, we make use of the following partition formula

[tex]B = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Substitute known values

[tex]B = (\frac{3 \times 5 + 1\times 2}{3+1},\frac{3\times 9 + 1 \times 6}{3+1})[/tex]

[tex]B = (\frac{17}{4},\frac{33}{4})[/tex]

[tex]B = (4.25,8.25)[/tex]

Hence, the location of B is: [tex](4.25,8.25)[/tex]

A segment with endpoints A (2, 6) and C (5,9) is partitioned by a point B such that AB and BC form a 3:1 ratio. Find B. (5 points) A.) (3.66, 7.66) B.) (4.25, 8.25) C.) (3.5, 10.5) D.) (2.33, 6.33)

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A segment with endpoints A (2, 6) and C (5,9) is partitioned by a point B such that AB
and BC form a 3:1 ratio. Find B. (5 points)
A.) (3.66, 7.66)
B.) (4.25, 8.25)
C.) (3.5, 10.5)
D.) (2.33, 6.33)