To determine the distance from point [tex]\(D\)[/tex] [tex]\((0, b)\)[/tex] to point [tex]\(A\)[/tex] [tex]\((0, 0)\)[/tex] in the coordinate plane, we can use the distance formula, which is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For points [tex]\(A\)[/tex] [tex]\((0, 0)\)[/tex] and [tex]\(D\)[/tex] [tex]\((0, b)\)[/tex]:
- [tex]\(x_1 = 0\)[/tex], [tex]\(y_1 = 0\)[/tex]
- [tex]\(x_2 = 0\)[/tex], [tex]\(y_2 = b\)[/tex]
Plugging the coordinates into the distance formula:
[tex]\[ \text{Distance} = \sqrt{(0 - 0)^2 + (b - 0)^2} \][/tex]
Simplify the expression inside the square root:
[tex]\[ \text{Distance} = \sqrt{0 + b^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{b^2} \][/tex]
[tex]\[ \text{Distance} = b \][/tex]
Therefore, the correct formula to determine the distance from point [tex]\(D\)[/tex] to point [tex]\(A\)[/tex] is:
[tex]\[ \text{Distance} = \sqrt{(0-0)^2+(b-0)^2} = \sqrt{b^2} = b \][/tex]
Thus, the correct choice is:
D. [tex]\(\sqrt{(0-0)^2+(b-0)^2}=\sqrt{b^2}=b\)[/tex]
