Consider the paragraph proof.

Given: D is the midpoint of AB, and E is the midpoint of AC.
Prove:DE = One-halfBC

On a coordinate plane, triangle A B C is cut by line segment D E. Point D is the midpoint of side A B and point E is the midpoint of side A C. Point A is at (2 b, 2 c), point E is at (a + b, c), point C is at (2 a, 0), point B is at (0, 0), and point D is at (b, c).

It is given that D is the midpoint of AB and E is the midpoint of AC. To prove that DE is half the length of BC, the distance formula, d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot, can be used to determine the lengths of the two segments. The length of BC can be determined with the equation BC = StartRoot (2 a minus 0) squared + (0 minus 0) squared EndRoot, which simplifies to 2a. The length of DE can be determined with the equation DE = StartRoot (a + b minus b) squared + (c minus c) squared EndRoot, which simplifies to ________. Therefore, BC is twice DE, and DE is half BC.

Which is the missing information in the proof?
a
4a
a2
4a2

Distance Formula for determining the distance between two points on a coordinate plane is given as: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

In the proof given, applying the distance formula to find DE, we have:

DE = √[(a + b - b)² + (c - c)²}

Simplifying this, we would have:

DE = √(a² + 0²) = √(a²)

DE = a

Therefore, the missing information in the proof is: A. a.

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wockstarrrrr wockstarrrrr · Answer 2 · 2022-07-24T19:59:12+02:00

wockstarrrrr wockstarrrrr

24-07-2022

Answer: A.

Step-by-step explanation:

a

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