Question

a point q on a segment with endpoints a (2, -1) and c (4, 2) partitions the segment in a 4:1 ratio. find q. you must show all work to receive credit.

Explanation:

Step1: Use the section formula

If a point \(Q(x,y)\) divides the line segment joining \(A(x_1,y_1)\) and \(C(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(x_1 = 2,y_1=-1,x_2 = 4,y_2 = 2,m = 4,n = 1\).

Step2: Calculate the \(x\) - coordinate of \(Q\)

Substitute the values into the \(x\) - formula:
\(x=\frac{4\times4+1\times2}{4 + 1}=\frac{16 + 2}{5}=\frac{18}{5}=3.6\)

Step3: Calculate the \(y\) - coordinate of \(Q\)

Substitute the values into the \(y\) - formula:
\(y=\frac{4\times2+1\times(-1)}{4 + 1}=\frac{8-1}{5}=\frac{7}{5}=1.4\)

Answer:

The coordinates of point \(Q\) are \((3.6,1.4)\)