To find the distance \( d \) between two points \( C \) and \( D \) with coordinates \( (-1, 4) \) and \( (2, 0) \) respectively, we will use the distance formula:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let’s go through the steps to find this distance:
1. Identify coordinates:
- \( x_1 = -1 \)
- \( y_1 = 4 \)
- \( x_2 = 2 \)
- \( y_2 = 0 \)
2. Calculate the differences:
- Difference in the x-coordinates (\( \Delta x \)):
[tex]\[
\Delta x = x_2 - x_1 = 2 - (-1) = 2 + 1 = 3
\][/tex]
- Difference in the y-coordinates (\( \Delta y \)):
[tex]\[
\Delta y = y_2 - y_1 = 0 - 4 = -4
\][/tex]
3. Square the differences:
- Square of \( \Delta x \):
[tex]\[
(\Delta x)^2 = 3^2 = 9
\][/tex]
- Square of \( \Delta y \):
[tex]\[
(\Delta y)^2 = (-4)^2 = 16
\][/tex]
4. Sum of the squared differences:
[tex]\[
(\Delta x)^2 + (\Delta y)^2 = 9 + 16 = 25
\][/tex]
5. Calculate the distance:
[tex]\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{25} = 5
\][/tex]
Therefore, the distance between points \( C(-1, 4) \) and \( D(2, 0) \) is
[tex]\[
\boxed{5} \text{ units}.
\][/tex]
