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.

The coordinates of the point Q are (3.5, 1.25)

Step-by-step explanation:

Okay , we want to find the coordinates of point Q that divides the line segment in that particular ratio.

To get the coordinates of Q, we use a particular division formula;

Let’s say we have the division ratio as a:b

Then the coordinates of point Q are as follows;

bx1 + ax2/(a+ b) , by1 + ay2/(a+b)

Where in the question;

a = 3

b = 1

x1 = 2

y1 = -1

x2 = 4

y2 = 2

Now plugging these values in the equation written above, we have;

1(2) + 3(4)/(3 + 1), 1(-1)+3(2)/(3+1)

(2+12)/4 , (-1+6)/4

= 14/4, 5/4

= (3.5, 1.25)