To find the distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex] with the given coordinates, we will use the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
The coordinates for point [tex]\( C \)[/tex] are [tex]\( (x_1, y_1) = (-1, 4) \)[/tex], and the coordinates for point [tex]\( D \)[/tex] are [tex]\( (x_2, y_2) = (2, 0) \)[/tex].
Substitute these coordinates into the distance formula:
[tex]\[ d = \sqrt{(2 - (-1))^2 + (0 - 4)^2} \][/tex]
First, simplify inside the parentheses:
[tex]\[ x_2 - x_1 = 2 - (-1) = 2 + 1 = 3 \][/tex]
[tex]\[ y_2 - y_1 = 0 - 4 = -4 \][/tex]
Now, square these differences:
[tex]\[ (x_2 - x_1)^2 = 3^2 = 9 \][/tex]
[tex]\[ (y_2 - y_1)^2 = (-4)^2 = 16 \][/tex]
Next, add these squared differences:
[tex]\[ 9 + 16 = 25 \][/tex]
Finally, take the square root of this sum:
[tex]\[ d = \sqrt{25} = 5 \][/tex]
The distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is [tex]\( 5 \)[/tex] units.
