Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.