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

The correct option is A.

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:

`((x_1+x_2)/(2),(y_1+y_2)/(2))`

The midpoint of AB is

`D=((0+x_1)/(2),(0+y_1)/(2))` (Using the midpoint formula)

The midpoint of AB is

`E=((x_1+x_2)/(2),(0+y_1)/(2))` (Using the midpoint formula)

Slope Formula:

`m=(y_2-y_1)/(x_2-x_1)`

The slope of DE is

`m=((0+y_1)/(2)-(0+y_1)/(2))/((x_1+x_2)/(2)-(0+x_1)/(2))=0`

The slope of AC is

`m=(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.