Question

question
what are the coordinates of the point on the directed line segment from (-3, -1) to (7, -6) that partitions the segment into a ratio of 1 to 4?
answer
you have 10 7 questions len to the your score.

Explanation:

Step1: Recall the section formula

The section formula for a point \((x,y)\) that divides the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2 + ny_1}{m + n}\). Here, \((x_1,y_1)=(-3,-1)\), \((x_2,y_2)=(7,-6)\), \(m = 1\), \(n = 4\).

Step2: Calculate the x - coordinate

Substitute the values into the x - coordinate formula: \(x=\frac{1\times7+4\times(-3)}{1 + 4}=\frac{7-12}{5}=\frac{-5}{5}=-1\)

Step3: Calculate the y - coordinate

Substitute the values into the y - coordinate formula: \(y=\frac{1\times(-6)+4\times(-1)}{1 + 4}=\frac{-6-4}{5}=\frac{-10}{5}=-2\)

Answer:

\((-1,-2)\)