A line has distance sqrt(13) how do I divide in into ratio 2:3 ?

Question

My questio nis

I have the points (1,2) nad (-2,4) and I have to find the co-ords of a point that divides them in a ratio of 2:3

If my high school maths still stands by me, the distance is sqrt(13)

Is that even relevant, because how would I find the point ?

Answer 1

Use this theory:

If a point P(x, y) divides a line segment joining points A(x1, y1) and B(x2, y2) in a ration m : n internally, Then,

x = (mx2 + nx1)/(m + n)
y = (my2 + ny1)/(m + n)

Now solve your problem:
Here,
x1 = 1
x2 = -1
y1 = 2
y2 = -4
m = 2
n = 3

Let the point dividing the line segment be P whose co-ordinates are (x, y)

Now find x and y with the given formula and thereby the co-ordinates of P. You have all the info you need. Distance isn't necessary.

x = [2(-2) + 3]/ 2 + 3
x = -1/5

y = [2(4) + 3(2)]/5
y = 14/5

The co-ordinates of the point are (-1/5, 14/5)

Answer 2

If you take the points, and consider only one of the co-ordinates at a time, you get:

x: -2, 1
y: 4, 2

You don't actually need to use the distance formula here.

Basically, in total there will be 5 sections, correct?
So, the first section is 2/5 of the way, and the latter 3/5.

Just deal with the x and y separately.

x:
The distance between -2 and 1 is 3, and 2/5 of this is 6/5.
Therefore, the x-co-ordinate will be at -2 + 6/5, which is -4/5.

y:
The distance between 4 and 2 is 2, and 2/5 of this is 4/5.
Therefore, the y-co-ordinate will be at 4 - 4/5, which is 3 1/5.

Thus, your co-ordinates are:
(-4/5, 3 1/5)

Answer 3

no it's not relevant.

just divide it vertical separation and horizontal separation between the 2 points by the ratio desired (2:3).

by my math that means the co-ord is (-0.2,2.8).

Answer 4

USE SECTION FORMULA.
X = [ m(X1) + n(X2) ] / (m+n)
Y = [ m(Y1) + n(Y2) ] / (m+n)
WHERE
(X1,Y1) & (X2,Y2) ARE COODINATES WHICH ARE JOINED
AND n:m IS THE RATIO OF INTERNAL BIJECTION.

SO , YOUR QUESTION

X = [3(1) +2(-2)]/(2+3)
= -1/5
&
Y = 14/5
THE COORDINATES ARE(-1/5 , 14/5)
SO DISTANCE FROM (1,2) IS
SQRT(52/25)

Answer 5

You are right. The number (2√13)/5 comes to me, but I am stymied how to use it.
http://www.mathworld.wolfram.com