Question

Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2,-3).

Answer 1

Answer:

Step-by-step explanation:

Solution: We have A = (4, -1) and B = (-2, -3)

Here;  x 1 = 4 x1=4 ,  y 1 = − 1 y1=-1 ,  x 2 = − 2 x2=-2  and  y 2 = − 3 y2=-3

Let us assume that points C and D divide line segment AB into three equal parts so that AC = CD = DB

In that case, point C divides AB in ratio 1 : 2 and point D divides AB in ratio 2 : 1

For point C; m1=1m1=1 and m2=2m2=2

For point D; m1=2m1=2 and m2=1m2=1  

Coordinates of point C can be calculated as follows:  

x=m1x2+m2x1m1+m2x=m1x2+m2x1m1+m2  

=1×−2+2×43=1×-2+2×43  

=−2+83=63=2=-2+83=63=2  

y=m1y2+m2y1m1+m2y=m1y2+m2y1m1+m2  

=1×−3+2×−13=1×-3+2×-13  

=−3−23=−53=-3-23=-53

Coordinates of point D can be calculated as follows:

x=m1x2+m2x1 m1+m2x=m1x2+m2x1m1+m2  

=2×−2+1×43=2×-2+1×43  

=−4+43=0=-4+43=0  

y=m1y2+m2y1m1+m2y=m1y2+m2y1m1+m2  

2×−3+1×−132×-3+1×-13  

=−6−13=−73=-6-13=-73

Hence; C=(2, −53)C=(2, -53) and D=(0, −73)D=(0, -73)