Question

A point Q on a segment with endpoints A(2, −1) and C(4, 2) partitions the segment in a 3:1 ratio. Find Q. You must show all work to receive credit. (10 points)

Answer 1

Given:

There are given that the two points:

$A(2,-1)\text{ and C(4, 2)}$

And,

The segment is:

$3\colon1$

Explanation:

To find the point Q, we need to use the segment formula.

From the formula:

$Q=(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2})$

Where,

$x_1=2,y_1=-1,x_2=4,y_2=2,m_1=3,m_2=1$

Then,

Put all the values into the above formula

So,

$\begin{gathered} Q=(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}) \\ Q=(\frac{3_{}(4)_{}+1_{}(2)_{}}{3_{}+1_{}},\frac{3_{}(2)_{}+1_{}(-1)_{}}{3_{}+1_{}}) \end{gathered}$

Then,

$\begin{gathered} Q=(\frac{3_{}(4)_{}+1_{}(2)_{}}{3_{}+1_{}},\frac{3_{}(2)_{}+1_{}(-1)_{}}{3_{}+1_{}}) \\ Q=(\frac{12_{}+2_{}}{4_{}},\frac{6_{}-1_{}_{}}{4_{}}) \\ Q=(\frac{14_{}}{4_{}},\frac{5_{}}{4_{}}) \\ Q=(\frac{7_{}}{2_{}},\frac{5_{}}{4_{}}) \end{gathered}$

Final answer:

Hence, the point Q is shown below:

$Q(\frac{7_{}}{2_{}},\frac{5_{}}{4_{}})$