Question
On a coordinate plane, point E is (negative 6, 8), point A is (5, 7), point B is (10, negative 2), point C is (8, negative 6), point D is negative 6, negative 6).
Which statements are true? Select all that apply
The length of side ED is equal to the length of side DC.
The length of side EA is equal to the length of side AB.
You can find the length of side BC by counting.
Shape ABCDE is a pentagon.
Shape ABCDE is a hexagon.
Which statements are true? Select all that apply
The length of side ED is equal to the length of side DC.
The length of side EA is equal to the length of side AB.
You can find the length of side BC by counting.
Shape ABCDE is a pentagon.
Shape ABCDE is a hexagon.
Answers
GPT-4o mini
To evaluate the statements regarding the coordinates of the points and the shape formed by them, let's analyze each option one by one.
1. **The length of side ED is equal to the length of side DC.**
- **Points:** E(-6, 8) and D(-6, -6)
- Length of ED = |8 - (-6)| = 14
- **Points:** D(-6, -6) and C(8, -6)
- Length of DC = |-6 - (-6)| = 14
- **Comparison:** Yes, **ED = DC**, so this statement is TRUE.
2. **The length of side EA is equal to the length of side AB.**
- **Points:** E(-6, 8) and A(5, 7)
- Length of EA = √[(5 - (-6))² + (7 - 8)²] = √[(11)² + (-1)²] = √(121 + 1) = √122
- **Points:** A(5, 7) and B(10, -2)
- Length of AB = √[(10 - 5)² + (-2 - 7)²] = √[(5)² + (-9)²] = √(25 + 81) = √106
- **Comparison:** EA ≠ AB, so this statement is FALSE.
3. **You can find the length of side BC by counting.**
- **Points:** B(10, -2) and C(8, -6)
- **Horizontal movement:** From x = 10 to x = 8, a distance of 2 units to the left.
- **Vertical movement:** From y = -2 to y = -6, a distance of 4 units down.
- Using the distance formula: Length of BC = √[(8 - 10)² + (-6 - (-2))²] = √[(-2)² + (-4)²] = √(4 + 16) = √20.
- Since it is not a straight line along the grid, the length cannot simply be counted as it involves diagonal movement. Therefore, this statement is FALSE.
4. **Shape ABCDE is a pentagon.**
- The points E, A, B, C, D form 5 vertices. A shape with 5 sides is a pentagon.
- So, this statement is TRUE.
5. **Shape ABCDE is a hexagon.**
- A hexagon has 6 sides and 6 vertices. Shape ABCDE has only 5 vertices.
- So, this statement is FALSE.
### Summary of True Statements:
- The length of side ED is equal to the length of side DC. (TRUE)
- Shape ABCDE is a pentagon. (TRUE)
**Final selections:**
- The length of side ED is equal to the length of side DC.
- Shape ABCDE is a pentagon.
1. **The length of side ED is equal to the length of side DC.**
- **Points:** E(-6, 8) and D(-6, -6)
- Length of ED = |8 - (-6)| = 14
- **Points:** D(-6, -6) and C(8, -6)
- Length of DC = |-6 - (-6)| = 14
- **Comparison:** Yes, **ED = DC**, so this statement is TRUE.
2. **The length of side EA is equal to the length of side AB.**
- **Points:** E(-6, 8) and A(5, 7)
- Length of EA = √[(5 - (-6))² + (7 - 8)²] = √[(11)² + (-1)²] = √(121 + 1) = √122
- **Points:** A(5, 7) and B(10, -2)
- Length of AB = √[(10 - 5)² + (-2 - 7)²] = √[(5)² + (-9)²] = √(25 + 81) = √106
- **Comparison:** EA ≠ AB, so this statement is FALSE.
3. **You can find the length of side BC by counting.**
- **Points:** B(10, -2) and C(8, -6)
- **Horizontal movement:** From x = 10 to x = 8, a distance of 2 units to the left.
- **Vertical movement:** From y = -2 to y = -6, a distance of 4 units down.
- Using the distance formula: Length of BC = √[(8 - 10)² + (-6 - (-2))²] = √[(-2)² + (-4)²] = √(4 + 16) = √20.
- Since it is not a straight line along the grid, the length cannot simply be counted as it involves diagonal movement. Therefore, this statement is FALSE.
4. **Shape ABCDE is a pentagon.**
- The points E, A, B, C, D form 5 vertices. A shape with 5 sides is a pentagon.
- So, this statement is TRUE.
5. **Shape ABCDE is a hexagon.**
- A hexagon has 6 sides and 6 vertices. Shape ABCDE has only 5 vertices.
- So, this statement is FALSE.
### Summary of True Statements:
- The length of side ED is equal to the length of side DC. (TRUE)
- Shape ABCDE is a pentagon. (TRUE)
**Final selections:**
- The length of side ED is equal to the length of side DC.
- Shape ABCDE is a pentagon.