To find the distance between points [tex]\(C\)[/tex] and [tex]\(D\)[/tex] with coordinates [tex]\(C(-1, 4)\)[/tex] and [tex]\(D(2, 0)\)[/tex], we will use the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's denote [tex]\(C\)[/tex] as [tex]\((x_1, y_1) = (-1, 4)\)[/tex] and [tex]\(D\)[/tex] as [tex]\((x_2, y_2) = (2, 0)\)[/tex].
First, calculate the differences in the coordinates:
[tex]\[ x_2 - x_1 = 2 - (-1) \][/tex]
[tex]\[ x_2 - x_1 = 2 + 1 \][/tex]
[tex]\[ x_2 - x_1 = 3 \][/tex]
[tex]\[ y_2 - y_1 = 0 - 4 \][/tex]
[tex]\[ y_2 - y_1 = -4 \][/tex]
Now, substitute these differences back into the distance formula:
[tex]\[ d = \sqrt{(3)^2 + (-4)^2} \][/tex]
[tex]\[ d = \sqrt{9 + 16} \][/tex]
[tex]\[ d = \sqrt{25} \][/tex]
[tex]\[ d = 5 \][/tex]
Thus, the distance between points [tex]\(C\)[/tex] and [tex]\(D\)[/tex] is [tex]\(\boxed{5}\)[/tex] units.
