Mathematics: Since the slope of Line segment DE and Line segment AC are identical, Line segment DE and Line segment AC are parallel by the definition of parallel lines. Which statement corrects the flaw in Gina s proof?

Since the slope of Line segment DE and Line segment, №9080693, 17.06.2020 20:39

Mathematics

Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side: given: δabc prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac. draw δabc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). point d is the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2. the quantity

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P Answered by Master

Hello,
Please, see the attached files.
Thanks.
Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a

Mathematics

Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side: given: δabc prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac. draw δabc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). point d is the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2. the quantity

Step-by-step answer

P Answered by Master

7

The answers are

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

(ii) The coordinates of D and E were found using the Midpoint Formula.

Step-by-step explanation: We can easily see in the proof that the co-ordinates of D and E were found using the mid-point formula, not distance between two points formula. So, this is the first flaw in the Gina's proof.

Also, we see that the slope of line DE and AC, both are same, not equal to 0 but is equal to

$\dfrac{y_2}{x_2},$

which is 0 only if y_2=0.

So, this is the second mistake.

Thus, the statements that corrects the flaw in Gina's proof are

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

(ii) The coordinates of D and E were found using the Midpoint Formula.

Mathematics

gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side. given: ∆abc prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac. draw ∆abc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). label point d as the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2; the quantity

Step-by-step answer

P Answered by PhD

28

What is the flaw in Gina’s proof?
A) Points D and E must be constructed, not simply labeled, as midpoints.

B) Segments DE and AC are parallel by construction. THIS IS THE FLAW. THE SEGMENTS WERE NOT DRAWN NOR PROPERLY IDENTIFIED.

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

Mathematics

Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side: given: δabc prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac. draw δabc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). point d is the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2. the quantity

Step-by-step answer

P Answered by Master

14

The coordinates of D and E were found using the Midpoint Formula.

Mathematics

Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side: given: δabc prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac. draw δabc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). point d is the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2. the quantity

Step-by-step answer

P Answered by Master

11

Hello! I hope I can be of some assistance on this question! Anyways,

It is a simple and fun geometrical problem, and it makes all sense until: "The slope of Line segment DE is found to be 0 through the application of the slope formula:" After that it gets all confusing etc. The slope formula applied to DE is simply:(difference between the y coordinates) divided by (difference of the x coordinates).In this case, by construction, D and E have the same y coordinate equal to y1 / 2.Therefore the slope is zero. Using the same technique, you will find that the slope of segment AC is also zero (by construction obviously since point A is the origin (0,0) and point C is on the x-axis. Therefore:The slope of segments DE and AC is not 0. = INCORRECTSegments DE and AC are parallel by construction. = CORRECT (they have the same slope)The coordinates of D and E were found using the Midpoint Formula. = CORRECTThe coordinates of D and E were found using the slope formula. = INCORRECT Very confusing problem, but I hope this helps!

Mathematics

Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side: given: δabc prove: the midsegment between sides line segment ab and line segment bc is parallel to side line segment ac. draw δabc on the coordinate plane with point a at the origin (0, 0). let point b have the ordered pair (x1, y1) and locate point c on the x-axis at (x2, 0). point d is the midpoint of line segment ab with coordinates at ordered pair the quantity 0 plus x sub 1, divided by 2. the quantity

Step-by-step answer

P Answered by Specialist

11

Hello! I hope I can be of some assistance on this question! Anyways,

It is a simple and fun geometrical problem, and it makes all sense until: "The slope of Line segment DE is found to be 0 through the application of the slope formula:" After that it gets all confusing etc. The slope formula applied to DE is simply:(difference between the y coordinates) divided by (difference of the x coordinates).In this case, by construction, D and E have the same y coordinate equal to y1 / 2.Therefore the slope is zero. Using the same technique, you will find that the slope of segment AC is also zero (by construction obviously since point A is the origin (0,0) and point C is on the x-axis. Therefore:The slope of segments DE and AC is not 0. = INCORRECTSegments DE and AC are parallel by construction. = CORRECT (they have the same slope)The coordinates of D and E were found using the Midpoint Formula. = CORRECTThe coordinates of D and E were found using the slope formula. = INCORRECT Very confusing problem, but I hope this helps!

Mathematics

Imran is paid ?286 per week Every week he puts 20% of his wage into a savings account How much does he put into his savings each week

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P Answered by PhD

The answer is in the image