Final answer:
The coordinates of point R on line segment PQ are calculated to be (5, -3) based on the formula for partitioning a line segment in a ratio of 3:1. However, this result is not listed among the given options.
Step-by-step explanation:
To find the coordinates of point R that is 3/4 the distance from P to Q, we can use the concept of partitioning a line segment in a given ratio, which in this case is 3:1. Here, P is given by the coordinates (-4,6) and Q by (8,-6).
To find the x-coordinate of R, we use the formula:
x_R = (1 - t)x_P + t*x_Q
Where t is the fraction of the distance from point P to Q, which is 3/4 in this instance. Plugging in the values gives us:
x_R = (1 - 3/4)(-4) + (3/4)(8) = (1/4)(-4) + 6 = -1 + 6 = 5
Similarly, to find the y-coordinate of R:
y_R = (1 - 3/4)y_P + t*y_Q
y_R = (1/4)(6) + (3/4)(-6) = 1.5 - 4.5 = -3
Therefore, the coordinates of point R are (5, -3), which is not given in any of the options. Hence, the correct coordinates seem to be missing from the options provided.