The x - coordinate of the point is [tex]x=-2[/tex]
Explanation:
Given that the coordinates of the two points J and K are (-6,-2) and (8,-9)
We need to determine the x - coordinate of the point that divides the directed line segment from J to K into a ratio of 2 : 5
The value of the x - coordinate can be determined using the formula,
[tex]x=\frac{m}{m+n} (x_2-x_1)^2+x_1[/tex]
where m = 2, n = 5 and [tex]x_1=-6[/tex] and [tex]x_2=8[/tex] in the above formula, we get,
[tex]x=\frac{2}{2+5} (8+6)+(-6)[/tex]
Simplifying, we get,
[tex]x=\frac{2}{7} (14)-6[/tex]
Dividing the terms, we get,
[tex]x=2(2)-6[/tex]
Multiplying the terms, we have,
[tex]x=4-6[/tex]
Subtracting, we get,
[tex]x=-2[/tex]
Thus, the x - coordinate of the point is [tex]x=-2[/tex]
