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Centroid

Centroid. Equation of AD (median) Strategy…. Find midpoint D Find eq’n of AD by Find slope “m” of AD using A & D Plug “m” & point A or D into y= mx+b & solve for “b” Now write eq’n using “m” & “b”.

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Centroid

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  1. Centroid • Equation of AD (median) • Strategy…. • Find midpoint D • Find eq’n of AD by • Find slope “m” of AD using A & D • Plug “m” & point A or D into y=mx+b & solve for “b” • Now write eq’n using “m” & “b” Remember – the centroid is useful as the centre of the mass of a triangle – you can balance a triangle on a centroid!

  2. Centroid Eq’n AD – Midpoint of BC

  3. Centroid Eq’n AD – Slope of AD

  4. Centroid Eq’n AD – Finding “b”

  5. Centroid Eq’n AD – Equation

  6. Orthocentre • Equation of altitude AD • Strategy…. • Find “m” of BC • Take –ve reciprocal of “m” of BC to get “m” of AD • Find eq’n of AD by • Plug “m” from 2. & point A into y=mx+b & solve for “b” • Now write eq’n using “m” & “b”

  7. Orthocentre Eq’n AD – Slope of BC then Slope of AD

  8. Orthocentre Eq’n AD – Finding “b”

  9. Orthocentre Eq’n AD – Equation

  10. Circumcenter • Equation of ED (perpendicular bisector) • Strategy… (use A (-1, 4), B (-1, -2) & C(5, 1)) • Find midpoint D • Find eq’n of ED by • Find slope “m” of BC using B & E • Take –ve reciprocal to get “m” of ED • Plug “m” ED & point D into y = mx+b & solve for b • Now write eq’n using “m” & “b”

  11. Circumcentre eq’n ED – Midpoint of BC

  12. Circumcentre Eq’n ED – Slope of BC & Slope of ED

  13. Circumcentre Eq’n ED – Finding “b”

  14. Circumcentre Eq’n ED – Equation

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