Answer:
0
Step-by-step explanation:
Given the points J (1,-10) and K (7, 2)
From the section formula
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
The y-coordinates of the point that divides the directed line segment from J to K into a ratio of 5:1 is obtained using the formula:
[tex]y=\dfrac{my_2+ny_1}{m+n}\\m=5, n=1, y_1=-10, y_2=2\\Therefore:\\y=\dfrac{5*2+1*-10}{5+1}\\=\dfrac{10-10}{6}\\=0[/tex]
The y-coordinates of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
The y coordinate of the point that divides J to K in the ratio 5 : 1 is 0.
If a point O(x, y) divides the line segment AB with end points A(x₁, y₁) and B(x₂, y₂) in the ratio n:m, the coordinate of O is:
[tex]x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1[/tex]
Let O(x, y) represent the point dividing J to K in the ratio 5 : 1. K(7,2) and J(1, -10)Hence:
[tex]y=\frac{5}{5+1}(2-(-10)) + (-10)=0[/tex]
The y coordinate of the point that divides J to K in the ratio 5 : 1 is 0.
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