To determine the distance between point [tex]\( C \)[/tex] with coordinates [tex]\((-1, 4)\)[/tex] and point [tex]\( D \)[/tex] with coordinates [tex]\( (2, 0) \)[/tex], we will use the distance formula. The distance formula is:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Here:
- [tex]\((x_1, y_1) = (-1, 4)\)[/tex] are the coordinates of point [tex]\( C \)[/tex],
- [tex]\((x_2, y_2) = (2, 0)\)[/tex] are the coordinates of point [tex]\( D \)[/tex].
Step-by-step procedure:
1. Calculate the difference in the x-coordinates ([tex]\(x_2 - x_1\)[/tex]):
[tex]\[
x_2 - x_1 = 2 - (-1) = 2 + 1 = 3
\][/tex]
2. Calculate the difference in the y-coordinates ([tex]\(y_2 - y_1\)[/tex]):
[tex]\[
y_2 - y_1 = 0 - 4 = -4
\][/tex]
3. Square the differences:
[tex]\[
(x_2 - x_1)^2 = 3^2 = 9
\][/tex]
[tex]\[
(y_2 - y_1)^2 = (-4)^2 = 16
\][/tex]
4. Sum the squares of the differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 9 + 16 = 25
\][/tex]
5. Take the square root of the sum to find the distance:
[tex]\[
d = \sqrt{25} = 5
\][/tex]
Thus, the distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is:
[tex]\[
\boxed{5}
\][/tex]
units.
