Question

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)

Answer 1

ANSWER

The correct answer is B.

EXPLANATION

If the point B(x,y) partitions

$A(x_1,y_1)$

and

$C(x_2,y_2)$

in the ratio m:n then, then we have

$x = \frac{mx_2+nx_1}{m + n}$

and

$y= \frac{my_2+ny_1}{m + n}$

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:

$x = \frac{5 \times 11+3 \times - 5}{5 + 3}$

$\implies \: x = \frac{55 - 15}{8}$

$\implies \: x = \frac{40}{8} = 5$

$y = \frac{5 \times 0 + 3 \times 2}{5 + 3}$

$y = \frac{0 + 6}{8}$

$y = \frac{6}{8} = \frac{3}{4}$

Therefore the coordinates of B are

$(5, \frac{3}{4} )$

Answer 2

Answer:

B. (5,3/4)

Step-by-step explanation:

Since, when a segment having end points $(x_1, y_1)$ and $(x_2, y_2)$ 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,

$(\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})$

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,

$(\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})$

$(\frac{55-15}{8}, \frac{0+6}{8})$

$(\frac{40}{8}, \frac{6}{8})$

$(5, \frac{3}{4})$

Option 'B' is correct.