Final answer:
The ratio in which the point (1, a) divides the line segment between (-1, 4) and (4, -1) is 1:4, which can be found using the section formula. The provided options do not accurately reflect this ratio since it is actually 4:1 with the segments reversed. The correct answer isn't given in the choices provided.
Step-by-step explanation:
To find the ratio in which the point (1, a) divides the line segment joining the points (-1, 4) and (4, -1), we can apply the section formula. The section formula states that if a point P(x, y) divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P are given by (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)). Since we know the x-coordinate of P is 1, we can set up the following equation based on the x-coordinates of A and B:
1 = (m * 4 + n * (-1)) / (m + n)
The y-coordinate is not needed for this problem because we are only looking for the ratio m:n, and we can determine it from the x-coordinate alone. After simplifying and solving for the ratio, we find that m:n is 1:4. However, the corresponding selection from the given options should be reversed to reflect the correct order asked in the question: 4:1. Therefore, none of the provided options (A, B, C, or D) are correct for the ratio 4:1.
Let's look at a simpler problem for an example of using a ratio:
Find the missing actual dimension if the scale factor is 1:4 and the scale measurement is 8 inches.
Solution:
1:4 = 8:x
Here, we can cross-multiply to solve for x:
1 * x = 4 * 8
x = 32 inches
This means the actual dimension corresponding to the 8-inch scale measurement is 32 inches when the scale factor is 1:4.