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In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line
x + y = 4?
The equation of the line joining the points (–1, 1) and (5, 7) is given by
The equation of the given line is
x + y – 4 = 0 … (2)
The point of intersection of lines (1) and (2) is given by
x = 1 and y = 3
Let point (1, 3) divide the line segment joining (–1, 1) and (5, 7) in the ratio 1:k. Accordingly, by section formula,
Thus, the line joining the points (–1, 1) and (5, 7) is divided by line
x + y = 4 in the ratio 1:2.
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