To determine the distance between the two points, we use the distance formula, which is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. For our specific case, the points are [tex]\((-2, 3)\)[/tex] and [tex]\((0, 0)\)[/tex].
Step-by-step solution:
1. Identify the coordinates:
[tex]\[ (x_1, y_1) = (-2, 3) \][/tex]
[tex]\[ (x_2, y_2) = (0, 0) \][/tex]
2. Calculate the differences between corresponding coordinates:
[tex]\[ x_2 - x_1 = 0 - (-2) = 0 + 2 = 2 \][/tex]
[tex]\[ y_2 - y_1 = 0 - 3 = -3 \][/tex]
3. Square these differences:
[tex]\[ (x_2 - x_1)^2 = 2^2 = 4 \][/tex]
[tex]\[ (y_2 - y_1)^2 = (-3)^2 = 9 \][/tex]
4. Sum the squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 4 + 9 = 13 \][/tex]
So, the number that goes beneath the radical symbol, representing the sum of the squared differences, is [tex]\( 13 \)[/tex].
