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.
