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)

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

step-by-step explanation: