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Find the gradient, equations and intersections of medians, altitudes and perpendicular bisectors using our knowledge of the mid-point as well as parallel and perpendicular lines.
Part ofMathsAlgebraic and geometric skills
Two non-parallel lines will have a common point -the point of intersection - where they cross each other or meet.
Find the point of intersection of the lines \(3y = 2x + 4\) and \(3x = 7 - 2y\)
Rearrange then use simultaneous equations to solve.
\(3y - 2x = 4\,( \times 3) \to 9y - 6x = 12\)
\(2y + 3x = 7\,( \times 2) \to 4y + 6x = 14\)
Add:
\(13y = 26\)
\(y = 2\)
Put \(y = 2\) in \(2y + 3x = 7\) which gives \(4 + 3x = 7\)
So \(3x = 3\) giving \(x = 1\)
\((1,2)\) is the point of intersection.
