the points r (0,1), i(2,−2), c(3,1) , ando(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 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. yes. i found the slopes of cap r cap iand and found that they had the same slope. i then found the slopes of cap i cap cand cap o cap r cap c cap o 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 cap r cap i cap c cap o 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 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 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.

Answer 1

To determine if the quadrilateral with vertices R(0,1), I(2,-2), C(3,1), and O(1,4) is a parallelogram, we can use a few different methods, such as checking for parallel sides (via slopes) and confirming if opposite sides are equal in length (using distance). The following options from your responses correctly indicate ways to confirm that quadrilateral RICO is a parallelogram:

1. Slope Method:

   • "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 the same slopes, it means that the opposite sides are parallel to each other. This proves that RICO is a parallelogram."

   This statement correctly identifies that parallel opposite sides confirm a parallelogram.

2. Distance Method:

   • "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."

   This statement correctly identifies that equal lengths of opposite sides also indicate a parallelogram.

3. Midpoint Method:

   • "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."

   This method establishes that if the diagonals bisect each other, the shape is indeed a parallelogram.

Thus, these options correctly affirm that the quadrilateral RICO is a parallelogram based on the identified properties.