To determine the distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex], we use the distance formula, which is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's identify the coordinates of points [tex]\( C \)[/tex] and [tex]\( D \)[/tex]:
- Point [tex]\( C \)[/tex] has coordinates [tex]\((x_1, y_1) = (-1, 4)\)[/tex].
- Point [tex]\( D \)[/tex] has coordinates [tex]\((x_2, y_2) = (2, 0)\)[/tex].
Next, we substitute these coordinates into the distance formula:
[tex]\[ d = \sqrt{(2 - (-1))^2 + (0 - 4)^2} \][/tex]
First, simplify the expressions inside the parentheses:
[tex]\[ d = \sqrt{(2 + 1)^2 + (0 - 4)^2} \][/tex]
This simplifies to:
[tex]\[ d = \sqrt{3^2 + (-4)^2} \][/tex]
Calculate the squares of these numbers:
[tex]\[ d = \sqrt{9 + 16} \][/tex]
Add these values together:
[tex]\[ d = \sqrt{25} \][/tex]
Finally, take the square root of 25:
[tex]\[ d = 5 \][/tex]
Thus, the distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is [tex]\(\boxed{5}\)[/tex] units.
