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The lines x−3y=5 and −3x−y=5 intersect at P. A third straight line, L, passes through the origin and has slope m. L intersects x−3y=5 at R, and −3x−y=5 at Q. The three lines are drawn in the following diagram.
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Show that x−3y=5 is perpendicular to −3x−y=5.
Find the coordinates of P.
Give expressions, in terms of the slope m of L, for the lengths
[PQ]
[PR]
It is given that area of triangle △PQR is 845units2, and that −3<m<31.
Find the possible value(s) of m.
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