Question

their ratios provided you know that A, Pand B are collinear.
Example 8 : Find the coordinates of the points of trisection (ie, points dividing in
three equal parts) of the line segment joining the points A(2,-2) and B(-7,4).​

Answer 1

Answer:

Given:- A line segment joining the points A(2,−2) 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+nmx 2 +nx 1 , m+nmy 2 +ny 1 )Therefore,

Coordinates of P=( 1+21×(−7)+2×2 , 1+21×4+2×(−2) )=(−1,0)Coordinates of Q=( 1+22×(−7)+1×2, 1+22×4+1×(−2) )=(−4,2)

Therefore, the coordinates of the points of trisection of the line segment joining A and B are (−1,0) and (−4,2).

Step-by-step explanation:

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