The coordinates of L are (3, 7), using the section formula.
According to the section formula, any line segment AB, with endpoints A(x₁, y₁) and B(x₂, y₂), when divided a point P internally in the ratio m:n, the coordinates of point P are given as:
P = ( {mx₁ + nx₂}/{m + n}, {my₁ + ny₂}/{m + n} ).
According to the question, we have A(x₁, y₁) = J(-4, -7), B(x₂, y₂) = K(4, 9), and the ratio m:n = 1:7.
The point that divided JK internally is L.
Thus, the coordinates of L can be shown as:
L = ( {1*(-4) + 7*4}/{1 + 7}, {1*(-7) + 7*9}/{1 + 7} ),
or, L = ( {-4 + 28}/8, {-7 + 63}/8 ),
or, L = ( 24/8, 56/8 ),
or, L = (3, 7).
Thus, the coordinates of L are (3, 7), using the section formula.
Learn more about the section formula at
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