Question

Find the coordinates of the points which trisect the line segment joining the points A(4, -3), B(9,7).​

Answer 1

Answer:

Step-by-step explanation:

Let the points P and Q which trisecets the line AB

P (x,y)&Q (r,s)

P intersect the line in ratio 1:2

&

Q intersect the line in ratio 2:1

We use section formula to find the coordinates of P & Q

First we find the coordinate of P (x,y)

x= m1x2+m2x1/m1+m2

x= 1×9+2×4/1+2

x= 9+8/3

x= 17/3

Now, y=m1y2 +m2y1 /m1+m2

y= 1×7+2×(-3)/1+2

y= 7+(-6)/3

y= 7-6/3

y=1/3

So,the coordinates of P is (17/3 ,1/3)

Now , we find the coordinates of Q (r,s)

r=m1x2+m2x1/m1+m2

r= 2×9+1×4/2+1

r= 18+4/3

r= 22/3

Now , s= m1y2 + m2y1/ m1+m2

s= 2×7+1×(-3)/1+2

s= 14+(-3)/3

s= 14-3/3

s= 11/3

Hence , the coordinates of Q is (22/3,11/3)

I HOPE THIS WILL HELP YOU