ruthannpearce2021
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Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.

A. (3, 1)
B. (5,3/4)
C. (10, 5)
D. (6, 2)

Respuesta :

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ANSWER

The correct answer is B.

EXPLANATION

If the point B(x,y) partitions

[tex]A(x_1,y_1)[/tex]

and

[tex]C(x_2,y_2)[/tex]

in the ratio m:n then, then we have

[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]

and

[tex]y= \frac{my_2+ny_1}{m + n} [/tex]

We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.

This implies that:

[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex]

[tex] \implies \: x = \frac{55 - 15}{8} [/tex]

[tex] \implies \: x = \frac{40}{8} = 5[/tex]

[tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex]

[tex]y = \frac{0 + 6}{8} [/tex]

[tex]y = \frac{6}{8} = \frac{3}{4} [/tex]

Therefore the coordinates of B are

[tex](5, \frac{3}{4} )[/tex]

Answer:

B. (5,3/4)

Step-by-step explanation:

Since, when a segment having end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is divided by or partitioned by a point, that lies on the segment, in the ratio of m : n,

Then the coordinates of that points are,

[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})[/tex]

Here, point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3,

Thus, the coordinates of B are,

[tex](\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})[/tex]

[tex](\frac{55-15}{8}, \frac{0+6}{8})[/tex]

[tex](\frac{40}{8}, \frac{6}{8})[/tex]

[tex](5, \frac{3}{4})[/tex]

Option 'B' is correct.

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