Question

find the coordinates of thepoints of trisection of the line segment joining the points A(-5,6) and B(4,3)​

Answer 1

Given,

The coordinates of the endpoints of the line segment are = A(-5,6) and B(4,3)

To find,

The coordinates of the points of the trisection of the given line segment.

Solution,

We can easily solve this mathematical problem, by the following process.

Let, the two points of trisection are = P and Q

Now, the line segment is divided into three equal parts.

So, the point P internally divides the AB line segment in the ratio of 1:2. And, the point Q divides the AB line segment in the ratio of 2:1.

Let,

P = X1,Y1

Q = X2,Y2

A = X3,Y3

B = X4,Y4

For the point P, the m:n = 1:2

Formula = (mX4 + nX3)/(m+n) , (mY4 + nY3)/(m+n)

So, value of X1 = [(1×4)+ (2)×(-5)]/(1+2) = (4-10)/3 = -6/3 = -2

Value of Y1 = [(1×3)+(2×6)](1+2) = (3+12)/3 = 15/3 = 5

Coordinate of P = (-2,5)

For the point Q, the m:n = 2:1

So, the value of X2 = [(2×4)+(1)×(-5)]/(2+1) = (8-5)/3 = 3/3 = 1

Value of Y2 = [(2×3)+(1×6)]/(2+1) = (6+6)/3 = 12/3 = 4

Coordinates of Q = (1,4)

Hence, the points of trisection are (-2,5) and (1,4).