Question

Question

The points R (0,1), I(2,−2), C(3,1)
, and O(1,4)
are the vertices of a quadrilateral. Is RICO
is a parallelogram? How do you know? (Select all that apply)(2 points)
Responses

Yes. I found the distance of RI
and CO
and found that they are the same distance. I then found the distance of IC
and OR
and they are also the same distance. Since they are the same distance, it means that the opposite sides are congruent to each other. This proves that RICO
is a parallelogram.
Yes. I found the distance of cap r cap iand cap c cap o and found that they are the same distance. I then found the distance of cap i cap cand cap o cap rand they are also the same distance. Since they are the same distance, it means that the opposite sides are congruent to each other. This proves that cap r cap i cap c cap o is a parallelogram.

No, RICO
is not a parallelogram.
No, cap r cap i cap c cap o is not a parallelogram.

Yes. I found the midpoint of the diagonals. They met at the same point so it means we have diagonals that are bisected. This means this is a parallelogram.
Yes. I found the midpoint of the diagonals. They met at the same point so it means we have diagonals that are bisected. This means this is a parallelogram.

Yes. I found the slopes of RI
and CO
and found that they had the same slope. I then found the slopes of IC
and OR
and they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that RICO
is a parallelogram.
Yes. I found the slopes of cap r cap iand cap c cap o and found that they had the same slope. I then found the slopes of cap i cap cand cap o cap rand they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that cap r cap i cap c cap o is a parallelogram.

Yes. I found the slope of IC
and OR
and the distance of IC
and OR
. I found that the slopes were the same which means that IC
and OR
are parallel and IC
and OR
are the same length. This allows me to prove that this forms a parallelogram
Yes. I found the slope of cap i cap c and cap o cap r and the distance of cap i cap c and cap o cap r. I found that the slopes were the same which means that cap i cap c and cap o cap r are parallel and cap i cap c and cap o cap r are the same length. This allows me to prove that this forms a parallelogram

Yes. I found the slopes of RI
and and found that they had the same slope. I then found the slopes of IC
and OR
CO
and they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that RICO
is a parallelogram.

Answer 1

To determine if the quadrilateral RICO is a parallelogram, you can use different methods of verification, such as checking the lengths of opposite sides, the midpoints of the diagonals, or the slopes of opposite sides.

The correct responses that would lead to the conclusion that RICO is a parallelogram are:

1. Midpoint of the Diagonals:

   • "Yes. I found the midpoint of the diagonals. They met at the same point so it means we have diagonals that are bisected. This means this is a parallelogram."

2. Lengths of Opposite Sides:

   • "Yes. I found the distance of RI and CO and found that they are the same distance. I then found the distance of IC and OR and they are also the same distance. Since they are the same distance, it means that the opposite sides are congruent to each other. This proves that RICO is a parallelogram."

3. Slopes of Opposite Sides:

   • "Yes. I found the slopes of RI and CO and found that they had the same slope. I then found the slopes of IC and OR and they also had the same slope. Since they have same slopes, it means that the opposite sides are parallel to each other. This proves that RICO is a parallelogram."

Any of these methods could confirm that RICO is a parallelogram, as they are all valid ways to prove the properties of a parallelogram. Therefore, the first three responses related to these methods are correct choices.