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Question
Find the coordinates of the points which divide the line segment joining 𝐴(𝟐, −𝟑) and 𝐵(−𝟒, −𝟔) into three equal parts.
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Solution
Let P & Q be the points of trisection. Then AP:PB = 1:2 & AQ:QB = 2:1
(i) Let P divides AB in ratio 1:2
Hence m1=1,m2=2,x1=2,
y1=−3,x2=−4andy2=−6.
(ii) Let Q divides AB in ratio 2:1
Here m1=2,m2=1,x1=2,y1=−3,x2=−4andy2=−6.
Q(−2, −5)
∴ Hence the coordinates of points of trisection are (0,0) & (−2,−5).
(i) Let P divides AB in ratio 1:2
Hence m1=1,m2=2,x1=2,
y1=−3,x2=−4andy2=−6.
(ii) Let Q divides AB in ratio 2:1Here m1=2,m2=1,x1=2,y1=−3,x2=−4andy2=−6.
Q(−2, −5)∴ Hence the coordinates of points of trisection are (0,0) & (−2,−5).
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