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Question

Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

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Solution

From the figure, it can be observed that points X, Y, Z are dividing the line segment in a ratio 1:3, 1:1, 3:1 respectively.
Coordinates of X=(1×2+3×(2)1+3,1×8+3×21+3)
=(1,72)
Coordinates of Y=(2+(2)2,2+82)
=(0,5)
Coordinates of Z=(3×2+1×(2)3+1,3×8+1×23+1)
=(1,132)

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