To determine the distance between the points [tex]\(C(-4, -2)\)[/tex] and [tex]\(D(3, 5)\)[/tex], we can use the distance formula. The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
First, identify the coordinates of the points:
- [tex]\(C(x_1, y_1) = (-4, -2)\)[/tex]
- [tex]\(D(x_2, y_2) = (3, 5)\)[/tex]
Next, calculate the differences in the x and y coordinates:
- [tex]\(\Delta x = x_2 - x_1 = 3 - (-4) = 3 + 4 = 7\)[/tex]
- [tex]\(\Delta y = y_2 - y_1 = 5 - (-2) = 5 + 2 = 7\)[/tex]
Now, apply these differences to the distance formula:
[tex]\[
\text{Distance} = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(7)^2 + (7)^2} = \sqrt{49 + 49} = \sqrt{98}
\][/tex]
Taking the square root of 98, we get approximately:
[tex]\[
\sqrt{98} \approx 9.899494936611665
\][/tex]
So, the distance between the points [tex]\(C(-4, -2)\)[/tex] and [tex]\(D(3, 5)\)[/tex] is approximately [tex]\(9.899494936611665\)[/tex]. Given the options, [tex]\(9.8\)[/tex] is the closest to this value.
Thus, the distance is approximately:
[tex]\[
\boxed{9.8}
\][/tex]
