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Question
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
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Solution
Since, the points P, Q, R and S divide the line segment joining the points
A (1,2) and B ( 6,7) in five equal parts, so
AP = PQ = QR = R = SB
Here, point P divides AB in the ratio of 1 : 4 internally So using section formula, we get
`"Coordinates of P "= ((1xx(6) +4xx(1))/(1+4) = (1 xx(7) +4xx(2))/(1+4))`
`= ((6+4)/5 , (7+8)/5) = (2,3)`
The point Q divides AB in the ratio of 2 : 3 internally. So using section formula, we get
`"Coordinates of Q " =((2 xx(6) +3 xx(1))/(2+3) = (2xx(7) +3xx(2))/(2+3))`
`= ((12+3)/5 , (14+6)/5) = (3,4)`
The point R divides AB in the ratio of 3 : 2 internally So using section formula, we get
`"Coordinates of R " = ((3 xx(6) +2 xx(1))/(3+2) = (3xx(7) +2 xx(2))/(3+2))`
`= ((18+2)/5 = (21+4)/5) = (4,5)`
Hence, the coordinates of the points P, Q and R are (2,3) , (3,4) and (4,5) respectively
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