Unit 2 - Triangles Equilateral Triangles

Trainer/Instructor Notes: Triangles The Meeting Place
3 19
8 −( − )
2 19
=
2
= −
0 −1 −1
2
7 −11
−2− 2 11
=
2
= −
3 13 13
5 −( − )
2 2
The equation of the median from A to
BC is y = 19 y =
− x +8
2
11 − x +b.
13
Substitute (5, –2) to solve for b.
11
−2= − ⋅ 5+b
13
Simplifying: b = 29
13 .
The equation of the median from C to
11 29
AB is y = − x+ .
13 13
Find the intersection point by substitution:
19 11 29
− x +8 = − x+ .
2 13 13
19 11 29
− x + x = − 8.
2 13 13
225 150
− x= − .
26 26
2
2
x = . Substitute x = in y =
3 3 19 − x +8.
2
19 2 5
y= − ⋅ +8=
.
2 3 3
11 29
Check in the other equation: y = − x+ =
13 13
11 2 29 22 87 65 5
− ⋅ + = − + = = .
13 3 13 39 39 39 3
2 5
The centroid is ( , )
3 3 .
Orthocenter:
Slope of BC:
−1−( −2)
1
=
−3−5 − 8
.
Perpendicular slope = 8.
Slope of AB :
8 −( −1)
9
= =3.
0 −( −3)
3
Perpendicular slope = 1
−
3
Geometry Module 2-28