Question

Consider a line segment AB with the endpoints A(11, 3) and B. What are the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2?

Answer 1

The coordinates of the point that divides the line segment AB in the ratio of 1:2 are (8, 4).

To find the coordinates of the point that divides the line segment AB in the ratio of 1:2, we can use the section formula, which is given by:

`\[ P(x, y) = \left((m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2)\right) \]`

Here,
`\(m_1\) and \(m_2\)` are the ratios in which the line segment is divided.

Given that the ratio is 1:2, we have
`\(m_1 = 1\) and \(m_2 = 2\)`.

The coordinates of A are
`\(A(11, 3)\)`, and the coordinates of B are \(B(2, 6)\).

Now, substitute these values into the formula:

`\[ P(x, y) = \left((1 * 2 + 2 * 11)/(1 + 2), (1 * 6 + 2 * 3)/(1 + 2)\right) \]`

`\[ P(x, y) = \left((2 + 22)/(3), (6 + 6)/(3)\right) \]`

`\[ P(x, y) = \left((24)/(3), (12)/(3)\right) \]`

`\[ P(x, y) = (8, 4) \]`

So, the coordinates of the point that divides the line segment AB in the ratio of 1:2 are (8, 4).

Therefore, the correct answer is:

c. (8, 4)

Complete question:

Line segment ab has endpoints A(11, 3) and B(2, 6). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1:2.

a.(4, 6)

b.(6, 4)

c. (8, 4)

d.( 20 3 , 4)