Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine whether the distances between points A and B (denoted as AB) and between points B and C (denoted as BC) are equal, we need to calculate each distance separately using the distance formula:
The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
1. Calculate the distance AB:
- Coordinates of A: [tex]\((0, 3)\)[/tex]
- Coordinates of B: [tex]\((2, 7)\)[/tex]
[tex]\[ AB = \sqrt{(2 - 0)^2 + (7 - 3)^2} \][/tex]
Simplifying inside the square root:
[tex]\[ AB = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.472 \][/tex]
2. Calculate the distance BC:
- Coordinates of B: [tex]\((2, 7)\)[/tex]
- Coordinates of C: [tex]\((6, 8)\)[/tex]
[tex]\[ BC = \sqrt{(6 - 2)^2 + (8 - 7)^2} \][/tex]
Simplifying inside the square root:
[tex]\[ BC = \sqrt{4^2 + 1^2} = \sqrt{16 + 1} = \sqrt{17} \approx 4.123 \][/tex]
3. Comparison of distances AB and BC:
- Distance AB ≈ 4.472
- Distance BC ≈ 4.123
Since 4.472 is not equal to 4.123, we can conclude that [tex]\( AB \neq BC \)[/tex].
Thus, the statement "AB = BC" is False.
The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
1. Calculate the distance AB:
- Coordinates of A: [tex]\((0, 3)\)[/tex]
- Coordinates of B: [tex]\((2, 7)\)[/tex]
[tex]\[ AB = \sqrt{(2 - 0)^2 + (7 - 3)^2} \][/tex]
Simplifying inside the square root:
[tex]\[ AB = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.472 \][/tex]
2. Calculate the distance BC:
- Coordinates of B: [tex]\((2, 7)\)[/tex]
- Coordinates of C: [tex]\((6, 8)\)[/tex]
[tex]\[ BC = \sqrt{(6 - 2)^2 + (8 - 7)^2} \][/tex]
Simplifying inside the square root:
[tex]\[ BC = \sqrt{4^2 + 1^2} = \sqrt{16 + 1} = \sqrt{17} \approx 4.123 \][/tex]
3. Comparison of distances AB and BC:
- Distance AB ≈ 4.472
- Distance BC ≈ 4.123
Since 4.472 is not equal to 4.123, we can conclude that [tex]\( AB \neq BC \)[/tex].
Thus, the statement "AB = BC" is False.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.