Certainly! To find the coordinates of the point that is [tex]\(\frac{1}{3}\)[/tex] of the way from point [tex]\(A(-7, -2)\)[/tex] to point [tex]\(B(2, 4)\)[/tex], we can follow these steps:
1. Determine the horizontal and vertical distances between the points [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
- Horizontal distance: [tex]\(B_x - A_x = 2 - (-7) = 2 + 7 = 9\)[/tex]
- Vertical distance: [tex]\(B_y - A_y = 4 - (-2) = 4 + 2 = 6\)[/tex]
2. Calculate [tex]\(\frac{1}{3}\)[/tex] of these distances:
- [tex]\(\frac{1}{3}\)[/tex] of the horizontal distance: [tex]\(\frac{1}{3} \cdot 9 = 3\)[/tex]
- [tex]\(\frac{1}{3}\)[/tex] of the vertical distance: [tex]\(\frac{1}{3} \cdot 6 = 2\)[/tex]
3. Add these distances to the coordinates of point [tex]\(A\)[/tex] to find the desired point:
- Horizontal coordinate: [tex]\(A_x + 3 = -7 + 3 = -4\)[/tex]
- Vertical coordinate: [tex]\(A_y + 2 = -2 + 2 = 0\)[/tex]
Therefore, the coordinates of the point that is [tex]\(\frac{1}{3}\)[/tex] of the way from [tex]\(A(-7,-2)\)[/tex] to [tex]\(B(2,4)\)[/tex] are [tex]\((-4, 0)\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{(-4, 0)} \][/tex]
