Medians - Perp Bisectors - Altitudes

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Presentation transcript:

Medians - Perp Bisectors - Altitudes The coordinates of DABC are A(2, 2), B(12, 4), C(6, 10). Determine the length of the median from A to side BC. C(6, 10) Find midpoint of side BC. M(9, 7) M = (9, 7) B(12, 4) A(2, 2) Join AM

Find the length of AM. C(6, 10) M(9, 7) B(12, 4) A(2, 2)

The coordinates of DPQR are P(-5,0), Q(3, 7), R(7, 1) The coordinates of DPQR are P(-5,0), Q(3, 7), R(7, 1). Determine the equation of the median from P to side QR. Find the midpoint of QR. Q(3, 7) M(5, 4) M = (5, 4) R(7, 1) P(–5, 0) Join MP

y = mx + b Determine the equation of MP. Q(3, 7) M(5, 4) R(7, 1)

y = mx + b 4 = 2 + b 2 = b Determine the equation of MP. sub (5,4) to find b Q(3, 7) M(5, 4) 4 = 2 + b R(7, 1) 2 = b P(–5, 0)

Determine the equation of the perpendicular bisector of AB Determine the equation of the perpendicular bisector of AB. A(–5, 6) B(7, –2) (The perpendicular bisector passes through the midpoint and is perpendicular to AB) A(–5, 6) l M = (1, 2) The slope of the perpendicular bisector is the negative reciprocal slope of AB. M(1, 2) B(7, –2) Find slope of AB …

sub in M(1,2) A(–5, 6) l M(1, 2) The slope of l is B(7, –2)

Draw the altitude from A. The coordinates of DABC are A(–3,7), B(–6, 0), C(4, 4). Find the equation of the altitude from A. Draw the altitude from A. A(–3, 7) Find slope of BC C(4, 4) D B(–6, 0)

Determine the equation of AD C(4, 4) D B(–6, 0)