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Question
Q is a point on the line segment AB. The coordinates of A and B are (2, 7) and (7, 12) along the line AB so that AQ = 4BQ. Find the coordinates of Q.
Solution
AQ : BQ = 4 : 1
Coordinates of Q are
Q (x , y) = Q `((4 xx 7 + 1xx 2)/(4 + 1) , (4 xx 12 + 1 xx 7)/(4 + 1))` = Q (6 , 11)
Thus the coordinates of Q are (6,11)
AQ = `sqrt ((2 - 6)^2 + (7 - 11)^2) = sqrt (16 + 16) = 4 sqrt 2`
BQ = `sqrt ((7 - 6)^2 + (12 - 11)^2) = sqrt (1 + 1) = sqrt 2`
⇒ AQ = 4 BQ
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