Question

partitioning a segment
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determine the coordinates of point p on ab such that the ratio of ap to pb is 1:3.
(1 point)

Explanation:

Step1: Use the section formula

If a point \(P(x,y)\) divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), then the coordinates of \(P\) are given by \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(A=(0,-5)\), \(B=(0,-1)\), \(m = 1\), \(n = 3\).

Step2: Calculate the \(y\) - coordinate (since \(x\) - coordinate of \(A\) and \(B\) is \(x = 0\))

For the \(y\) - coordinate, substitute \(y_1=-5\), \(y_2=-1\), \(m = 1\), \(n = 3\) into the formula \(y=\frac{my_2+ny_1}{m + n}\).

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The \(x\) - coordinate of \(P\) is \(x = 0\) (because \(A\) and \(B\) lie on the line \(x = 0\)).

Answer:

\((0,-4)\)