Question
quadrilateral has vertices located at
B
(
1
,
3
)
,
R
(
−
6
,
2
)
,
H
(
−
5
,
5
)
,
B(1,3), R(−6,2), H(−5,5), and
W
(
0
,
0
)
.
W(0,0).
Drag and drop to complete the statement.
Quadrilateral is a because .
DRAG & DROP THE ANSWER
RWBH
RHWB
BRHW
rhombus
parallelogram
rectangle
diagonals are congruent and opposite sides are congruent
diagonals are perpendicular
diagonals are not congruent
Note: Use CTRL+D to drag the option via keyboard
B
(
1
,
3
)
,
R
(
−
6
,
2
)
,
H
(
−
5
,
5
)
,
B(1,3), R(−6,2), H(−5,5), and
W
(
0
,
0
)
.
W(0,0).
Drag and drop to complete the statement.
Quadrilateral is a because .
DRAG & DROP THE ANSWER
RWBH
RHWB
BRHW
rhombus
parallelogram
rectangle
diagonals are congruent and opposite sides are congruent
diagonals are perpendicular
diagonals are not congruent
Note: Use CTRL+D to drag the option via keyboard
Answers
GPT-4o mini
To classify the quadrilateral formed by the vertices \( B(1,3) \), \( R(-6,2) \), \( H(-5,5) \), and \( W(0,0) \), we need to analyze the properties of the shape.
1. **Calculating the lengths of the sides**:
- Distance \( BR \):
\[
d(BR) = \sqrt{(1 - (-6))^2 + (3 - 2)^2} = \sqrt{(1 + 6)^2 + (3 - 2)^2} = \sqrt{7^2 + 1^2} = \sqrt{49 + 1} = \sqrt{50}
\]
- Distance \( RH \):
\[
d(RH) = \sqrt{(-6 - (-5))^2 + (2 - 5)^2} = \sqrt{(-6 + 5)^2 + (2 - 5)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]
- Distance \( HW \):
\[
d(HW) = \sqrt{(-5 - 0)^2 + (5 - 0)^2} = \sqrt{(-5)^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50}
\]
- Distance \( WB \):
\[
d(WB) = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]
2. **Analyzing pairs of lengths**:
From the above calculations:
- \( BR \) and \( HW \) (both \(\sqrt{50}\)) are equal.
- \( RH \) and \( WB \) (both \(\sqrt{10}\)) are equal.
3. **Properties of diagonals**:
To check the diagonals, we calculate the midpoint of \( BR \) and \( HW \), as well as \( RH \) and \( WB \).
---
### Properties determined:
- Opposite sides are equal: \( BR = HW \) and \( RH = WB \).
- Both pairs of opposite sides are equal, which suggests it is a parallelogram.
### Conclusion:
Since opposite sides are equal and there are no indications that either set of diagonals are perpendicular (as we haven't calculated slopes or angles), we conclude:
**Quadrilateral RWBH is a parallelogram because opposite sides are congruent.**
This matches:
**Drag and drop the final statement:**
Quadrilateral **RWBH** is a **parallelogram** because **diagonals are not congruent and opposite sides are congruent.**
(You may select a different form of the statement based on the options provided but the general classification remains as a parallelogram based on the equidistance of the opposing pairs.)
1. **Calculating the lengths of the sides**:
- Distance \( BR \):
\[
d(BR) = \sqrt{(1 - (-6))^2 + (3 - 2)^2} = \sqrt{(1 + 6)^2 + (3 - 2)^2} = \sqrt{7^2 + 1^2} = \sqrt{49 + 1} = \sqrt{50}
\]
- Distance \( RH \):
\[
d(RH) = \sqrt{(-6 - (-5))^2 + (2 - 5)^2} = \sqrt{(-6 + 5)^2 + (2 - 5)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]
- Distance \( HW \):
\[
d(HW) = \sqrt{(-5 - 0)^2 + (5 - 0)^2} = \sqrt{(-5)^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50}
\]
- Distance \( WB \):
\[
d(WB) = \sqrt{(0 - 1)^2 + (0 - 3)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]
2. **Analyzing pairs of lengths**:
From the above calculations:
- \( BR \) and \( HW \) (both \(\sqrt{50}\)) are equal.
- \( RH \) and \( WB \) (both \(\sqrt{10}\)) are equal.
3. **Properties of diagonals**:
To check the diagonals, we calculate the midpoint of \( BR \) and \( HW \), as well as \( RH \) and \( WB \).
---
### Properties determined:
- Opposite sides are equal: \( BR = HW \) and \( RH = WB \).
- Both pairs of opposite sides are equal, which suggests it is a parallelogram.
### Conclusion:
Since opposite sides are equal and there are no indications that either set of diagonals are perpendicular (as we haven't calculated slopes or angles), we conclude:
**Quadrilateral RWBH is a parallelogram because opposite sides are congruent.**
This matches:
**Drag and drop the final statement:**
Quadrilateral **RWBH** is a **parallelogram** because **diagonals are not congruent and opposite sides are congruent.**
(You may select a different form of the statement based on the options provided but the general classification remains as a parallelogram based on the equidistance of the opposing pairs.)