To find the distance between the two points [tex]\( C \)[/tex] and [tex]\( D \)[/tex], we can use the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, the coordinates of point [tex]\( C \)[/tex] are [tex]\((-1, 4)\)[/tex], and the coordinates of point [tex]\( D \)[/tex] are [tex]\((2, 0)\)[/tex]. Let's break it down step by step:
1. Identify the coordinates:
- Point [tex]\( C \)[/tex] ( [tex]\( x_1, y_1 \)[/tex] ) = [tex]\((-1, 4)\)[/tex]
- Point [tex]\( D \)[/tex] ( [tex]\( x_2, y_2 \)[/tex] ) = [tex]\((2, 0)\)[/tex]
2. Calculate the differences in the x and y coordinates:
- [tex]\( \Delta x = x_2 - x_1 = 2 - (-1) = 3 \)[/tex]
- [tex]\( \Delta y = y_2 - y_1 = 0 - 4 = -4 \)[/tex]
3. Square each difference:
- [tex]\( (\Delta x)^2 = 3^2 = 9 \)[/tex]
- [tex]\( (\Delta y)^2 = (-4)^2 = 16 \)[/tex]
4. Sum the squares of the differences:
- [tex]\( (\Delta x)^2 + (\Delta y)^2 = 9 + 16 = 25 \)[/tex]
5. Take the square root of the sum to find the distance:
- [tex]\( d = \sqrt{25} = 5 \)[/tex]
So, the distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is [tex]\( 5 \)[/tex] units.
