Final answer:
To find the x-coordinate of the point that divides the line segment J(-6,-2) to K(8,-9) into a ratio of 2:5, we can use the section formula, which states that x = (x1*m + x2*n)/(m+n). Using this formula, we find that the x-coordinate is 8.
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) into a ratio of 2:5, we can use the concept of section formula. The formula states that the x-coordinate of the point is given by:
x = (x1*m + x2*n)/(m+n)
where x1 and x2 are the x-coordinates of the given points J and K respectively, and m and n are the ratio components (2 and 5 in this case).
Using the formula, we have:
x = (-6*2 + 8*5)/(2+5) = (16+40)/7 = 56/7 = 8
Therefore, the x-coordinate of the point that divides the segment into a ratio of 2:5 is 8.