Question

. Find the coordinates of the points of trisection
of the line segment joining the points
(7, 5) and (-2, -1).​

Answer 1

Step-by-step explanation:

Let A(7,−2) and B(1,−5) be the given points and P(x,y) and Q(x

′

,y

′

) are the points of trisection.

Step 1: Find the coordinate of P

Point P divides AB internally in the ratio 1:2

(x,y)=[

1+2

1(1)+2(7)

,

1+2

1(−5)+1(−2)

]

=(

3

1+14

,

3

−5−4

)=(

3

15

,

3

−9

)=(5,−3)

Step 2: Find the coordinate of Q.

Point Q is the mid-point PB.

(x

′

,y

′

)=((5+1)/2,(−3−5)/2)=(3,−4)

Therefore, the coordinates of the points of trisection are (5,−3) and (3,4).