Question

What is the reason for statement 3 in this proof?

A) using point-slope formula

B) definition of parallel lines

C) Transitive Property of Equality

D) Reflexive Property of Equality

E) definition of midpoint

Answer 1

The answer is E. definition of midpoint, since it defines the midpoint of x and y.

Answer 2

Answer:- E) definition of midpoint

Explanation :-

We can look at the second step in the statement which says that" point D is the mid point of AB and E the point of BC " .

And we know that definition of midpoint says that "If a point is a mid point of line segment with end points $(x_1,y_1)\ and\ (x_2,y_2)$

Then the coordinates of the mid point must be

$(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$."

And statement 3 say $D=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

and  $E=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$, where D and E are mid points .

Thus the reason for statement 3 must be the definition of mid point.