Question

question what are the coordinates of the point on the directed line segment from (-5,5) to (7,-4) that partitions the segment into a ratio of 2 to 1? answer attempt 1 out of 2 submit answer show examples

Explanation:

Step1: Recall the section - formula

The formula for the coordinates of 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 given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-5,y_1 = 5,x_2 = 7,y_2=-4,m = 2,n = 1\).

Step2: Calculate the \(x\) - coordinate

Substitute the values into the \(x\) - coordinate formula:
\[x=\frac{2\times7+1\times(-5)}{2 + 1}=\frac{14 - 5}{3}=\frac{9}{3}=3\]

Step3: Calculate the \(y\) - coordinate

Substitute the values into the \(y\) - coordinate formula:
\[y=\frac{2\times(-4)+1\times5}{2 + 1}=\frac{-8 + 5}{3}=\frac{-3}{3}=-1\]

Answer:

\((3,-1)\)