Question

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

Answer 1

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)

Answer 2

Step-by-step explanation:

Consider the problem 

Let, 

the points of intersection 

P(x1,y1,z1) and Q(x2,y2,z2) 

then, 

P divides AB in the ratio 1:2

And 

Q divides AB in the ratio 2:1 

therefore, 

(x1,y1,z1)=(35+4,3−8+2,33−6)

(x1,y1,z1)=(3,−2,−1)

(x2,y2,z2)=(310+2,3−16+1,36−3)

(x2,y2,z2)=(4,−5,1)

therefore, 

Points which trisects the line AB are (3,