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
Watch this video to learn about perpendicular lines.
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Show that the lines with equations \(4x + 2y - 8 = 0\) and \(2y = x + 1\) are perpendicular.
First rearrange each equation in the form \(y = mx + c\).
\(2y = x + 1\)
\(y = \frac{1}{2}x + \frac{1}{2}\)
Identify the first gradient:
\(gradient = \frac{1}{2}\)
\(4x + 2y - 8 = 0\)
\(2y = - 4x + 8\)
\(y = \frac{{ - 4}}{2}x + \frac{8}{2}\)
\(y = - 2x + 4\)
Identify the second gradient:
\(gradient = - 2\)
Complete the proof:
\({m_1} \times {m_2} = \frac{1}{2} \times ( - 2) = - 1\)
Hence lines are perpendicular.
