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Find the coordinates of the point C, if the point $B 12, 6$ divides the line segment joining the points $A (3, 5)$ and $C$ in the ratio 1: 3.

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− 7, 9

− 7, 1

− 5, 9

− 7, 5

answer is A.

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Detailed Solution

It is given that
Coordinates of point B is

12, 6

, point A is

3, 5

.B divides AC in the ratio of

1 : 3

.
Let the coordinates of C be (a, b).
We know that,
Section Formula for the coordinates

(x, y)

of a point O that break the line segment joining the points

A (x_{1}, y_{1}) and B (x_{2}, y_{2})

in the ratio

m_{1} : m_{2}

is given by,

x = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}

and

y = \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}}

.
Then, using the section rule, to establish a relationship in terms of a and b.

12, 6 = 1 × a + 3 × 3 1 + 3, 1 × b + 3 × 5 1 + 3 ⇒ 12, 6 = a + 9 4, b + 15 4

On Equating the respective coordinates to find a and b we get,

12 = a + 9 4 ⇒ a + 9 = 2 ⇒ a = − 7 Similarly, 6 = b + 15 4 ⇒ b + 15 = 24 ⇒ b = 9

So, the coordinates of C is

− 7, 9

.
Hence, option (1) is correct.

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