Question

2. Find the coordinates of the point which divides the line segment joining points
A(-3, 4) and B (13. 12) in the ratio 5:3.
​

Answer 1

(7 , 9)

Step-by-step explanation:

We are given that a point divides the line segment joining points A(-3 , 4) and B(13,12) in the ratio 5 : 3. We need to find the coordinates of the point.

Section formula is used to find coordinates of a point that divides the line segment. It is also used to find the ratio in which the line segment is divided.

⇒ x coordinate = m₁x₂ + m₂x₁ / m₁ + m₂

⇒ y coordinate = m₁y₂ + m₂y₁ / m₁ + m₂

Finding x and y coordinates of the point:

⇒ x = m₁x₂ + m₂x₁ / m₁ + m₂

⇒ x = [5 × 13 + 3 × (-3) / (5 + 3)]

⇒ x = (65 - 9) / 8

⇒ x = 56 / 8

⇒ x = 7

⇒ y = m₁y₂ + m₂y₁ / m₁ + m₂

⇒ y = [(5 × 12 + 3 × 4) / (5 + 3)]

⇒ y = (60 + 12) / 8

⇒ y = 72 / 8

⇒ y = 9

⇒ Coordinates = (x , y)

⇒ Coordinates = (7 , 9)

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