Find that coordinates of P that partitions directed line segment AB in a ratio of 1:3. A (-1, 2) B (7, 14) a (-1, 5) b (1, -5) c (1,5) d (5, 1)

Hence the coordinate of P are (5,13.5).

Step-by-step explanation:

Given:

The line segment  AB with point A≡(-1,2) and B≡(7,14)

To Find :

A point p coordinates as it divides seg AB in ratio of 1:3.

Solution:

Now we know the formula for the directed line segment as with ratio a:b

and coordinates of end points (x1,y1)and(x2,y2)

hence here values are ,

a=1 ,b=3 and x1=-1,y1=2 x2=7,y2=14

P≡[{(a*x1+b*x2)}/(a+b),{(a*y1+b*y2)}/(a+b)]

P≡[{(1*-1+3*7)}/(4),{(1*2+14*3)}/4]

p≡(20/4,54/4)

P≡(5,13.5)

Hence the coordiante of the P on directed line is at (5,13.5) as it divides in 1:3 ratio.

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

a

step-by-step explanation: