Question

What are the coordinates of the point on the direct line segment from (-5, -10) to (2, 4) that partitions the segment into a ratio of 2 to 5?

Answer 1

Answer:(-3,-6)

Explanation:

Answer 2

Now the given coordinates are,

(-4,10) and (2,-10)

Thus, we have,

x₁ = -4

y₁ = 10

x₂ = 2

y₂ = -10

Given ratio, m₁ : m₂ = 1 : 3

⇒ m₁ = 1; m₂ = 3

Let (x,y) be the coordinates of the point on the directed line segment from (-4,10) to (2,-10) that partitions the segment into a ratio of 1 to 3.

Since the section formula is given as,

So, x = (m₁x₁ + m₂x₂) / (m₁ + m₂)

y = (m₁y₁ + m₂y₂) / (m₁ + m₂)

Put the values,

x = [1(-4) + 3*2)] / (1 + 3) = (-4+6) / 4 = 2/4

⇒ x = 1/2

Similarly y = [1(10) + 3*(-10)] / (1 + 3) = (10-30) / 4 = -20/4

⇒ y = -5

So, the required coordinates are (1/2, -5)

Thus, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).