To find the distance between points \( C \) and \( D \) in the coordinate plane, we will use the distance formula, which is given by:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Given:
- Point \( C \) has coordinates \((-1, 4)\).
- Point \( D \) has coordinates \((2, 0)\).
First, identify the coordinates:
- \( x_1 = -1 \)
- \( y_1 = 4 \)
- \( x_2 = 2 \)
- \( y_2 = 0 \)
Next, calculate the differences \( x_2 - x_1 \) and \( y_2 - y_1 \):
[tex]\[
x_2 - x_1 = 2 - (-1) = 2 + 1 = 3
\][/tex]
[tex]\[
y_2 - y_1 = 0 - 4 = -4
\][/tex]
Now, substitute these differences into the distance formula:
[tex]\[
d = \sqrt{(3)^2 + (-4)^2}
\][/tex]
Calculate the squares:
[tex]\[
(3)^2 = 9
\][/tex]
[tex]\[
(-4)^2 = 16
\][/tex]
Add these squares together:
[tex]\[
9 + 16 = 25
\][/tex]
Finally, take the square root to find the distance:
[tex]\[
d = \sqrt{25} = 5
\][/tex]
Therefore, the distance between points \( C \) and \( D \) is:
[tex]\[
5 \text{ units}
\][/tex]
