Final answer:
The x-coordinate of the point that divides the line segment from J (-6, -2) to K (8, -9) in a ratio of 2:5 is calculated using the section formula to be -2.
Step-by-step explanation:
To find the x-coordinate of the point that divides the line segment from J (-6, -2) to K (8, -9) in a 2:5 ratio, you can use the section formula or the concept of internal division of a point in a line segment. This formula involves a weighted average of the x-coordinates of the points J and K, with weights corresponding to the given ratio.
The formula for the x-coordinate of a point dividing a line segment in a given ratio m:n is:
x = (mx2 + nx1) / (m + n)
Plugging in the given values:
x = (2 × 8 + 5 × (-6)) / (2 + 5)
x = (16 - 30) / 7
x = -14 / 7
x = -2
Thus, the x-coordinate of the required point that divides the line segment from J to K in a ratio of 2:5 is -2.