State whether the given statement is true or false.

If the value of k is 2, then the point $C (k, 4)$ divides the join of points $A (2, 6)$ divides the join of pointsand B(5, 1) in the ratio 2: 3.

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True

False

answer is B.

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Detailed Solution

We have been given,
If the value of k is 2, then the point C(k, 4) divides the join of points A(2, 6) and B(5, 1) in the ratio 2: 3.
Using the section formula,

m x 2 + n x 1 m + n, m y 2 + n y 1 m + n

We know, the points are

A (2, 6)

and

B (5, 1)

.
The given ratio is 2:3.
Substituting

m = 2, n = 3, x_{2} = 5, x_{1} = 2, y_{2} = 1, and y_{1} = 6

in the section formula,

(k, 4) = (\frac{10 + 6}{2 + 3}, \frac{2 + 18}{2 + 3})

(k, 4) = (\frac{16}{5}, 4)

Therefore, our statement is false.
The value of k is

\frac{16}{5}

.
Hence, option 2 is correct.

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