Final answer:
Using the section formula with a ratio of VW:WX = 1:4, the coordinates of W are calculated to be (-3,0), which is not in the provided list of options. There may be an error in the question or the options given.
Step-by-step explanation:
To find the coordinates of point W on the line segment VX in the given ratio of VW:WX = 1:4, we can use the section formula. This formula allows us to find the coordinates of a point dividing a segment into a particular ratio.
The coordinates of V are (-7,-2) and the coordinates of X are (13,8). Since point W divides VX in the ratio 1:4, we can apply the section formula:
W(x_w, y_w) = ((m*x_2 + n*x_1) / (m+n), (m*y_2 + n*y_1) / (m+n))
Where V=(x_1, y_1), X=(x_2, y_2), W=(x_w, y_w) and the ratio is n:m.
We plug in the values:
x_w = (4*(-7) + 1*(13)) / (4+1) = (-28+13) / 5 = -15/5 = -3
y_w = (4*(-2) + 1*(8)) / (4+1) = (-8+8) / 5 = 0/5 = 0
Therefore, the coordinates of W are (-3,0), which is not listed in the options provided by the student. It appears there may be a typo in the question or the provided options.