To find the distance between the points [tex]\((-13, 2)\)[/tex] and [tex]\( (2, 2) \)[/tex], we use the distance formula. The distance formula is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, the coordinates of the two points are:
- [tex]\((x_1, y_1) = (-13, 2)\)[/tex]
- [tex]\((x_2, y_2) = (2, 2)\)[/tex]
First, we calculate the difference in the x-coordinates:
[tex]\[ x_2 - x_1 = 2 - (-13) = 2 + 13 = 15 \][/tex]
Next, we calculate the difference in the y-coordinates:
[tex]\[ y_2 - y_1 = 2 - 2 = 0 \][/tex]
Now, we substitute these differences into the distance formula:
[tex]\[ \text{Distance} = \sqrt{(2 + 13)^2 + (2 - 2)^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{15^2 + 0^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{225 + 0} \][/tex]
[tex]\[ \text{Distance} = \sqrt{225} \][/tex]
[tex]\[ \text{Distance} = 15 \][/tex]
Therefore, the distance between the points [tex]\((-13, 2)\)[/tex] and [tex]\( (2, 2) \)[/tex] is [tex]\(\boxed{15}\)[/tex].
