Question

if segment kl has endpoints at k(1,8) and l(1, - 4), what are the coordinates of point m that divides \\( \overline { k l } \\) in the ratio 1:3, if point m is closer to point k than point l? enter your answer in this format (x,y). use the keypad to enter the answer in the box provided. the coordinates of point m is

Explanation:

Step1: Calculate the difference in y - coordinates

The formula for finding a point that divides a line - segment in the ratio \(m:n\) is given by \(y=\frac{my_2 + ny_1}{m + n}\) (when \(x\) - coordinates of the endpoints are the same). Here, \(K(1,8)\) and \(L(1,-4)\), \(m = 1\), \(n=3\), \(y_1 = 8\), \(y_2=-4\).
The difference in \(y\) - coordinates: \(\Delta y=y_2 - y_1=-4 - 8=-12\).

Step2: Use the section formula for \(y\) - coordinate

Since \(x\) - coordinates of \(K\) and \(L\) are the same (\(x = 1\)), we only need to find the \(y\) - coordinate of \(M\).
Using the section formula \(y=\frac{my_2+ny_1}{m + n}\), substituting \(m = 1\), \(n = 3\), \(y_1 = 8\), \(y_2=-4\)

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Answer:

\((1,5)\)