Question

given: △abc
prove: the medians of △abc are concurrent.
proof:

1. the vertices of △abc are unique points: a(x1,y1), b(x2,y2), and c(x3,y3).

reason: given

1. use rigid transformations to transform △abc into △abc.

reason: in the coordinate plane, any point can be moved to any other point using
what is step 10 in this proof?
a. statement: point p lies on line ae and line bf.
reason: algebra
b. statement: all three lines share point p.
reason: definition of midpoint
c. statement: point p lies on line cd.
reason: the coordinates of p satisfy the equation of line cd.
d. statement: two of the three medians share point p.
reason: using point - slope formula
e. statement: line ae and line bf are concurrent.
reason: definition of concurrence

Explanation:

Step1: Analyze the proof process

In a proof about concurrency of medians, the final step is usually stating the concurrency.

Step2: Check the options

Option E states "line \(A'E'\) and line \(B'F'\) are concurrent" which is the conclusion of the proof (after showing the point \(P\) lies on all three medians, the last step is stating the concurrency).

Answer:

E. Statement: line \(A'E'\) and line \(B'F'\) are concurrent. Reason: Definition of concurrence.