1.

Find the coordinates of points which trisect the line segment joining the point A(5,-3) and B (2,-9)​

Answer»

ong>Answer: (4, -5)

A trisection point on a line segment trisects that line segment into THREE equal parts.

Here,

1 : 2

A •------------•----------------------------• B

C

Given that,

A = (5, -3)

B = (2, -9)

C = (x, y)

Which means, The point c divides the line segment in the ratio 1 : 2 which is m : n

Using the section formula, we can find the COORDINATE of the point C,

⇒ Cₓ = ( mx₂ + nx₁ ) / (m + n)

⇒ Cₓ = (1 × 2 + 2 × 5) / (2 + 1)

⇒ Cₓ = (2 + 10) / 3

⇒ Cₓ = 12 / 3

⇒ Cₓ = 4

Here, We got the abscissa of the point C to be 4.

Let US find the ordinate now,

⇒ Cᵧ = ( my₂ + ny₁ ) / (m + n)

⇒ Cᵧ = ( 1 × -9 + 2 × -3 ) / (1 + 2)

⇒ Cᵧ = ( -9 - 6 ) / 3

⇒ Cᵧ = -15/3

⇒ Cᵧ = -5

So, we got the ordinate to be -5.

Hence, The point C is (4, -5)

Note:-

Abscissa = x

Ordinate = y

Coordinate = (Abscissa, Ordinate)


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