Homework Help: geometry

Posted by Ginny on Sunday, April 24, 2011 at 4:40pm.

Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20).
Find the coordinates of the centroid.
Find the coordinates of the circumcenter.
Find the coordinates of the orthocenter.
Find the equation of the line.

geometry - Henry, Monday, April 25, 2011 at 5:37pm
1. P(1,2), Q(25,2), R(10,20).

X = (1+25+10) / 3 = 12.

Y = (2+2+20) / 3 = 8.

C(12,8). = Coordinates of Centroid.

2. SIDE PQ:
Xo = (1+25) / 2 = 13.

Yo = (2+2) / 2 = 2.

M(13,2).

m = (2-2) / (25-1) = 0/24 = 0.

m2 = -1/0 = Undefined = slope of perpendicular bisector(P.B.).

Eq1: X = 13 = Eq of P.B. of PQ = a ver line.

SIDE PR:

Xo = (1+10) / 2 = 5.5.

Yo = (2+20) / 2 = 11.

M(5.5,11).

m = (20-2) / (10-1) = 2.

m2 = -1/2 = slope of P.B. of PR.

Y = (-1/2)*5.5 + b = 11,
-2.75 + b = 11,
b = 11 + 2.75 = 13.75.

Eq2: Y = -X/2 + 13.75 = P.B. OF PR.

Substitute 13 for X:
Y = -13/2 + 13.75 = 7.25.

C(13,7.25).=Coordinates of circumcenter

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