Find the coordinates of the point which divides the line segment join…

The correct answer is Option (1) → (7, 3)

To find the coordinates of the point $(x, y)$ that divides the line segment joining the points $A(x_1, y_1) = (4, -3)$ and $B(x_2, y_2) = (8, 5)$ internally in the ratio $m_1 : m_2 = 3 : 1$, we use the Section Formula:

$x = \frac{m_1x_2 + m_2x_1}{m_1 + m_2}$

$y = \frac{m_1y_2 + m_2y_1}{m_1 + m_2}$

Step-by-Step Calculation:

Identify the values:

• $x_1 = 4$, $y_1 = -3$
• $x_2 = 8$, $y_2 = 5$
• $m_1 = 3$, $m_2 = 1$

Calculate the x-coordinate:

$x = \frac{3(8) + 1(4)}{3 + 1}$

$x = \frac{24 + 4}{4}$

$x = \frac{28}{4} = 7$

Calculate the y-coordinate:

$y = \frac{3(5) + 1(-3)}{3 + 1}$

$y = \frac{15 - 3}{4}$

$y = \frac{12}{4} = 3$

Final Answer:

The coordinates of the point are $(7, 3)$.