Question

PLZ HELP & EXPLAIN WHY!
Which statement corrects the flaw in Gina's proof?

A.) The coordinates of D and E were found using the midpoint formula.

B.) Segments DE and AC are parallel by construction.

C.) The slope of segments DE and AC is not 0.

D.) The coordinates of D and E were found using the Distance between Two Points Postulate.

Answer 1

A.) The coordinates of D and E were found using the midpoint formula. :)

Answer 2

Answer:

The correct option is A.

Step-by-step explanation:

Given: ΔABC

Prove: Mid segment between sides AB and BC is parallel side AC.

Let the vertices of triangle are A(0,0), B(x₁,y₁) and C(x₂,0).

Midpoint Formula:

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

The midpoint of AB is

$D=(\frac{0+x_1}{2},\frac{0+y_1}{2})$                (Using the midpoint formula)

The midpoint of AB is

$E=(\frac{x_1+x_2}{2},\frac{0+y_1}{2})$                (Using the midpoint formula)

Slope Formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope of DE is

$m=\frac{\frac{0+y_1}{2}-\frac{0+y_1}{2}}{\frac{x_1+x_2}{2}-\frac{0+x_1}{2}}=0$

The slope of AC is

$m=\frac{0-0}{x_2-x_0}=0$

Slope of AC and DE are same, therefore the lines AC and DE are parallel because slope of two parallel lines are same.

The correct statement is "The coordinates of D and E were found using the midpoint formula".

Therefore the correct option is A.