Question

find the points of trisection of the line segment joining (-2,1) and (7,4) with explanation​

Answer 1

Step-by-step explanation:

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Find the point of tri-section of the line segment joining the points (−2,1) and (7,4)

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Solution

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Given:- A line segment joining the points A(−2,1) and B(7,4).

Let P and Q be the points on AB such that,

AP=PQ=QB

Therefore,

P and Q divides AB internally in the ratio 1:2 and 2:1 respectively.

As we know that if a point (h,k) divides a line joining the point (x

1

,y

1

) and (x

2

,y

2

) in the ration m:n, then coordinates of the point is given as-

(h,k)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Therefore,

Coordinates of P=(

1+2

1×7+2×(−2)

,

1+2

1×4+2×1

)=(1,2)

Coordinates of Q=(

1+2

2×7+1×(−2)

,

1+2

2×4+1×1

)=(4,3)

Therefore, the coordinates of the points of trisection of the line segment joining A and B are (1,2) and (4,3).