Final answer:
To find the coordinates of a point 3/4 of the way between two given points, use a proportion. The x-coordinate is found by taking 3/4 of the difference between the x-coordinates of the points and adding it to the x-coordinate of the starting point. The y-coordinate is found in the same way but using the y-coordinates.
Step-by-step explanation:
To find the coordinates of a point that is 3/4 of the way from point A(-6, -1) to point B(14, 11), we need to use a proportion. We can find the x-coordinate by taking 3/4 of the difference between the x-coordinates of A and B, and adding it to the x-coordinate of A. Similarly, we can find the y-coordinate by taking 3/4 of the difference between the y-coordinates of A and B, and adding it to the y-coordinate of A.
Using the formula, the x-coordinate is:
x = -6 + (3/4)(14 - (-6)) = -6 + (3/4)(20) = -6 + 15 = 9
And the y-coordinate is:
y = -1 + (3/4)(11 - (-1)) = -1 + (3/4)(12) = -1 + 9 = 8
Therefore, the coordinates of the point 3/4 of the way from A to B are (9, 8), which corresponds to option D.