Question

find the coordinates of the point that partitions (overline{ab}) in the ratio (3:7).
the point that partitions (overline{ab}) in the ratio (3:7) is (square). (simplify your answer. type an ordered pair.)

Explanation:

Step1: Use the section formula

The section formula for a point \(P(x,y)\) that divides the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(A(-4,-7)\), \(B(12,5)\), \(m = 3\), \(n=7\).

Step2: Calculate the \(x\) - coordinate

Substitute \(x_1=-4\), \(x_2 = 12\), \(m = 3\), \(n = 7\) into \(x=\frac{mx_2+nx_1}{m + n}\).

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Step3: Calculate the \(y\) - coordinate

Substitute \(y_1=-7\), \(y_2 = 5\), \(m = 3\), \(n = 7\) into \(y=\frac{my_2+ny_1}{m + n}\).

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Answer:

\((0.8,-3.4)\)