Question

find the coordinates of the point which divides the line segment joining point A(-3,4) and B(13,12) in the ratio 5:3
please answer it fast as soon as possible​

Answer 1

(7,9)

Step-by-step explanation:

We are given two points: A(-3,4) and B(13,12) which is divided in the ratio of 5:3 by a point. According to the question, we need to find the coordinates of that point.

Section Formula: This formula is used to find two things:

1. Coordinates of a point which divides a line segment,
2. Ratio in which the line segment divides.

$\implies{\dfrac{m_1x_2+m_2x_1}{m_1+m_2}, \dfrac{m_1y_2+m_2y_1}{m_1+m_2}}$

From the given two points: A(-3,4) and B(13,12), we know that:

• $x_1 = -3$

• $x_2 = 13$

• $y_1 = 4$

• $y_2 = 12$

Since the ratio that divides the line segment is 5:3,

• $m_1 = 5$
• $m_2 = 3$

Let us apply the values in section formula:

$\implies{\dfrac{(5)(13)+(3)(-3)}{5+3}, \dfrac{(5)(12)+(3)(4)}{5+3}}$

$\implies{\dfrac{65-9}{8}, \dfrac{60+12}{8}}$

$\implies{\dfrac{56}{8}, \dfrac{72}{8}}$

$\implies{(7,9)}$

Hence, the coordinates is (7,9).