Point [tex]$C[tex]$[/tex] has the coordinates [tex]$[/tex](-1, 4)[tex]$[/tex] and point [tex]$[/tex]D[tex]$[/tex] has the coordinates [tex]$[/tex](2, 0)[tex]$[/tex]. What is the distance between points [tex]$[/tex]C[tex]$[/tex] and [tex]$[/tex]D$[/tex]?

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\square[/tex] units



Answer :

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]