18 What is the reason for statement in the given proof?
Ο Α.
definition of midpoint
Given: AABCProve: The medians of AABC are concurrent.
U
ов.
definition of slope
B' (2 2s)
OC. Parallel lines have equal slopes.
6
OD.
using point-slope formula
4
D'
2
All0.00
-2
C' (2,0)
14 16
-4
0
2
4
6 F
2.00
10
12
Statement
Reason
1. Define the vertices of AABC to have
unique points A(X1, 91), B(x2- y2), and
given
|C(x3, Y3).
in the coordinate plane,
any point can be moved
2. Use rigid transformations to to any other point using
transform AABC to AA'B'C so that A' is rigid transformations
at the origin and A'C' lies on the x- and any line can be
axis in the positive direction. moved to any other line
using rigid
transformations.
3. Any property that is true for AA'B'C' definition of
will also be true for AABC.
congruence
4. Let r, s, and t be real numbers such
that the vertices of AA'B'C' are A'(0, 0), defining constants
B'(2r, 2s), and C'(2t, O).
5. Let D'. E', and F be the midpoints of
A'B', B'C' and A'C' respectively.
defining points
6. D' = (r, s)
E' = (r + t, s)
definition of midpoints
F = (t,0)
AB=-*
7. slope of
2
21-
slope of 2=
8. equation of line A'E': Y=**
equation of line B'F',
23
making use of point-
y=2=X+2r-1
slope formula
slope of
B'p
C'D
>
2st