Answer:
Rounded to the nearest thousandth, the coordinates of point C are approximately (-2, 7.667).
Explanation:
To find the coordinates of point C that partitions line AB at a 6:3 ratio, we can use the concept of linear interpolation.
First, let's calculate the differences in the x- and y-coordinates between points A and B:
Δx = xB - xA = -6 - (-3) = -3
Δy = yB - yA = 10 - 3 = 7
Since we want to divide the line AB at a 6:3 ratio, we can express this as a proportion:
6/9 = x/Δx
Simplifying the proportion, we have:
2/3 = x/(-3)
Cross-multiplying, we get:
2 * (-3) = 3x
-6 = 3x
Dividing both sides by 3, we find:
x = -6/3 = -2
Now, let's calculate the corresponding y-coordinate for point C:
yC = yA + (2/3) * Δy
= 3 + (2/3) * 7
= 3 + (14/3)
= 23/3
Rounded to the nearest thousandth, the coordinates of point C are approximately (-2, 7.667).