Question

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

Explanation:

In a proof about the concurrency of medians (which are lines in a triangle), if two lines \(A'E'\) and \(B'F'\) intersect at a point \(P\), the next logical step is to show that the third line \(C'D'\) also passes through \(P\). When the coordinates of \(P\) satisfy the equation of line \(C'D'\), it means \(P\) lies on \(C'D'\). This is based on the fundamental concept that if a point's coordinates satisfy the equation of a line, then the point lies on that line.

Answer:

B. Statement: Point \(P\) lies on line \(C'D'\). Reason: The coordinates of \(P\) satisfy the equation of line \(C'D'\).