Question

Find the points of trisection of the line segment joining the points:

(a) 5, −6 and (−7, 5),

(b) (3, −2) and (−3, −4),

(c) (2, −2) and (−7, 4).

Answer 1

The co-ordinates of a point which divided two points and internally in the ratio is given by the formula,

The points of trisection of a line are the points which divide the line into the ratio.

(i) Here we are asked to find the points of trisection of the line segment joining the points A(5,−6) and B(−7,5).

So we need to find the points which divide the line joining these two points in the ratio and 2 : 1.

Let P(x, y) be the point which divides the line joining ‘AB’ in the ratio 1 : 2.

Let Q(e, d) be the point which divides the line joining ‘AB’ in the ratio 2 : 1.

Therefore the points of trisection of the line joining the given points are .

(ii) Here we are asked to find the points of trisection of the line segment joining the points A(3,−2) and B(−3,−4).

So we need to find the points which divide the line joining these two points in the ratio and 2 : 1.

Let P(x, y) be the point which divides the line joining ‘AB’ in the ratio 1 : 2.

Let Q(e, d) be the point which divides the line joining ‘AB’ in the ratio 2 : 1.

Therefore the points of trisection of the line joining the given points are.

(iii) Here we are asked to find the points of trisection of the line segment joining the points A(2,−2) and B(−7,4).

So we need to find the points which divide the line joining these two points in the ratio and 2 : 1.

Let P(x, y) be the point which divides the line joining ‘AB’ in the ratio 1 : 2.

Let Q(e, d) be the point which divides the line joining ‘AB’ in the ratio 2 : 1.

Therefore the points of trisection of the line joining the given points are .