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Centroid-Involves Finding Equation of the Median…

Centroid-Involves Finding Equation of the Median…. Equation of AD (median) Strategy …. Remember – the centroid is useful as the centre of the mass of a triangle – you can balance a triangle on a centroid!. Centroid-Involves Finding Equation of the Median…. Equation of AD (median)

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Centroid-Involves Finding Equation of the Median…

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  1. Centroid-Involves Finding Equation of the Median… Equation of AD (median) Strategy…. Remember – the centroid is useful as the centre of the mass of a triangle – you can balance a triangle on a centroid!

  2. Centroid-Involves Finding Equation of the Median… • 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!

  3. Centroid Eq’n AD – Midpoint of BC

  4. Centroid Eq’n AD – Slope of AD

  5. Centroid Eq’n AD – Finding “b”

  6. Centroid Eq’n AD – Equation

  7. Circumcenter-Involves Finding the Equation of the Perpendicular Bisector… • 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” Useful for finding the centre of the triangle, or a point in the middle of any three (x,y) points

  8. Circumcenter-Involves Finding the Equation of the Perpendicular Bisector… Equation of ED (perpendicular bisector) Strategy… (use A (-1, 4), B (-1, -2) & C(5, 1)) Useful for finding the centre of the triangle, or a point in the middle of any three (x,y) points

  9. Circumcentre eq’n ED – Midpoint of BC

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

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

  12. Orthocentre-Involves Finding the Equation of the Altitude • 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” Finding the equation of the altitude of a triangle is useful if you are asked to find the area

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

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

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