Answer :
To find the distance between points \( C \) with coordinates \((-1, 4)\) and \( D \) with coordinates \((2, 0)\), we will follow the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
### Step-by-Step Solution
1. Identify the Coordinates:
- Point \( C \): \( (x_1, y_1) = (-1, 4) \)
- Point \( D \): \( (x_2, y_2) = (2, 0) \)
2. Calculate the Differences:
- \( \Delta x = x_2 - x_1 = 2 - (-1) = 2 + 1 = 3 \)
- \( \Delta y = y_2 - y_1 = 0 - 4 = -4 \)
3. Square the Differences:
- \( (\Delta x)^2 = 3^2 = 9 \)
- \( (\Delta y)^2 = (-4)^2 = 16 \)
4. Sum of Squares:
[tex]\[ (\Delta x)^2 + (\Delta y)^2 = 9 + 16 = 25 \][/tex]
5. Calculate the Distance:
[tex]\[ d = \sqrt{25} = 5 \][/tex]
Therefore, the distance between points \( C \) and \( D \) is
[tex]\[ 5 \text{ units} \][/tex]
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
### Step-by-Step Solution
1. Identify the Coordinates:
- Point \( C \): \( (x_1, y_1) = (-1, 4) \)
- Point \( D \): \( (x_2, y_2) = (2, 0) \)
2. Calculate the Differences:
- \( \Delta x = x_2 - x_1 = 2 - (-1) = 2 + 1 = 3 \)
- \( \Delta y = y_2 - y_1 = 0 - 4 = -4 \)
3. Square the Differences:
- \( (\Delta x)^2 = 3^2 = 9 \)
- \( (\Delta y)^2 = (-4)^2 = 16 \)
4. Sum of Squares:
[tex]\[ (\Delta x)^2 + (\Delta y)^2 = 9 + 16 = 25 \][/tex]
5. Calculate the Distance:
[tex]\[ d = \sqrt{25} = 5 \][/tex]
Therefore, the distance between points \( C \) and \( D \) is
[tex]\[ 5 \text{ units} \][/tex]
