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Question
If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
Solution
Let the points P, Q, and R divide seg AB into four equal parts.
∴ AP = PQ = QR = RB
Point Q is the mid-point of seg AB.
∴ By mid-point formula,
`"x co-ordinate of Q" = (x_1 + x_2)/2 = (−14 + 6)/2 = (−8)/2 = −4`
`"y co-ordinate of Q" = (y_1 + y_2)/2 = (−10 + (−2))/2 = (−10 −2)/2 = (−12)/2 = − 6`
∴ Co-ordinates of Q are (−4, −6).
Point P is the mid-point of seg AQ.
∴ By mid-point formula,
`"x co-ordinate of P" = (x_1 + x_2)/2 = (−14 + (−4))/2 = (−14 −4)/2 = (−18)/2 = −9`
`"y co-ordinate of P" = (y_1 + y_2)/2 = (−10 + (−6))/2 = (−10 −6)/2 = (−16)/2 = −8`
∴ Co-ordinates of P are (−9, −8).
Point R is the mid-point of seg QB.
∴ By mid-point formula,
`"x co-ordinate of R" = (x_1 + x_2)/2 = (−4 + 6)/2 = 2/2 = 1`
`"y co-ordinate of R" = (y_1 + y_2)/2 = (−6 + (−2))/2 = (−6 −2)/2 = (−8)/2 = −4`
∴ Co-ordinates of R are (1, −4).
∴ The coordinates of the points dividing seg AB into four equal parts are P(−9, −8), Q(−4, −6), and R(1, –4).
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