To find the distance between the points [tex]\((-3, 2)\)[/tex] and [tex]\( (0, 3) \)[/tex], we can use the distance formula for two points in a plane. The distance formula is expressed as follows:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's identify and substitute the coordinates from the points into the formula:
- [tex]\( (x_1, y_1) = (-3, 2) \)[/tex]
- [tex]\( (x_2, y_2) = (0, 3) \)[/tex]
1. Calculate the differences in the x-coordinates ([tex]\( dx \)[/tex]) and y-coordinates ([tex]\( dy \)[/tex]):
[tex]\[ dx = x_2 - x_1 = 0 - (-3) = 3 \][/tex]
[tex]\[ dy = y_2 - y_1 = 3 - 2 = 1 \][/tex]
2. Square these differences:
[tex]\[ dx^2 = 3^2 = 9 \][/tex]
[tex]\[ dy^2 = 1^2 = 1 \][/tex]
3. Sum the squared differences:
[tex]\[ dx^2 + dy^2 = 9 + 1 = 10 \][/tex]
4. Take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{10} \][/tex]
Therefore, the distance between the points [tex]\((-3, 2)\)[/tex] and [tex]\( (0, 3) \)[/tex] is [tex]\( \sqrt{10} \)[/tex].
The correct choice is:
C. [tex]\( \sqrt{10} \)[/tex]
