MATH SOLVE

4 months ago

Q:
# Need help with this question! ☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺Julia is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning coordinates as given. Drag and drop the correct answer into each box to complete the proof.The coordinates of point C are (__, c).The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (__, c/2 ).The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are ( a+b/2, __).AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (a+b/2, c/2) .By the definition of midpoint, AE¯¯¯¯¯≅ __ and BE¯¯¯¯¯≅ __.Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other. Options: 1. a + b 2. a + c 3. b + c 4. a+b/2 5. a−b/2 6. a/2 7. b/2 8. c/2 9. AC¯¯¯¯¯ 10. BD¯¯¯¯¯ 11. CE¯¯¯¯¯ 12. DE¯¯¯¯¯

Accepted Solution

A:

1. Answer:a+b

The coordinates of point C are (__, c).

You can determine the length of the parallelogram by looking at the point B and point A. The length would be coordinate X of B minus X coordinate of A.

Parallerogram length= Xb- Xa

Parallerogram length= a-0= a

Then, the X coordinate of point C would be:

Xc= Xd + Parallerogram length

Xc= a+b

2. Answer: a+b/2

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (__, c/2 ).

The X and Y coordinate of midpoint of diagonal AC should be half of the X and Y coordinate of point C.

The midpoint would be:

Y= Yc/2

Y= c/2

X=Xc/2

X= a+b/2

Midpoint= (a+b/2, c/2)

3. Answer: c/2

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are ( a+b/2, __).

This question is similar to the number 2. The X coordinate would be more complicated but the question is asking for Y coordinate. The Y coordinate of the midpoint should be half of Y coordinate of point D minus Y coordinate of point B

Y= (Yd- Yb)/2

Y= (c-0)/2

Y= c/2

AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (a+b/2, c/2)--->not a question

4. Answer: AE≅ CE ; BE≅ DE

By the definition of midpoint, AE¯¯¯¯¯≅ __ and BE¯¯¯¯¯≅ __.

The length of AE should be half of AC. The length of AC should be sum of AE and EC. Then, AE should be equal to EC

AE= 1/2 AC

AC= AE+ CE

AC= 1/2 AC +CE

CE= AC- 1/2AC= 1/2 AC

CE=AE

The length of BE should be half of BD. The length of BD should be sum of BE and ED. Then, BE should be equal to ED

BE= 1/2 BD

BD= BE+ DE

BD= 1/2 BD +DE

DE= BD- 1/2BD = 1/2 BD

DE=1/2BD

DE=BE

Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other. --->not a question

The coordinates of point C are (__, c).

You can determine the length of the parallelogram by looking at the point B and point A. The length would be coordinate X of B minus X coordinate of A.

Parallerogram length= Xb- Xa

Parallerogram length= a-0= a

Then, the X coordinate of point C would be:

Xc= Xd + Parallerogram length

Xc= a+b

2. Answer: a+b/2

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (__, c/2 ).

The X and Y coordinate of midpoint of diagonal AC should be half of the X and Y coordinate of point C.

The midpoint would be:

Y= Yc/2

Y= c/2

X=Xc/2

X= a+b/2

Midpoint= (a+b/2, c/2)

3. Answer: c/2

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are ( a+b/2, __).

This question is similar to the number 2. The X coordinate would be more complicated but the question is asking for Y coordinate. The Y coordinate of the midpoint should be half of Y coordinate of point D minus Y coordinate of point B

Y= (Yd- Yb)/2

Y= (c-0)/2

Y= c/2

AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (a+b/2, c/2)--->not a question

4. Answer: AE≅ CE ; BE≅ DE

By the definition of midpoint, AE¯¯¯¯¯≅ __ and BE¯¯¯¯¯≅ __.

The length of AE should be half of AC. The length of AC should be sum of AE and EC. Then, AE should be equal to EC

AE= 1/2 AC

AC= AE+ CE

AC= 1/2 AC +CE

CE= AC- 1/2AC= 1/2 AC

CE=AE

The length of BE should be half of BD. The length of BD should be sum of BE and ED. Then, BE should be equal to ED

BE= 1/2 BD

BD= BE+ DE

BD= 1/2 BD +DE

DE= BD- 1/2BD = 1/2 BD

DE=1/2BD

DE=BE

Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other. --->not a question