More maths questions; help needed -> division of an Interval AB (1 Viewer)

[bouncing]

May you please help me out with these two questions...

10. The point P (11, -28) divided the interval AB in the ratio m:3. If A and B have coordinates (-1, 8) and (2, 1) respectively, find the value of m.

11. The point P (-10, 21) divides the interval AB with coordinates (-2, 5) and (2, -3) in the ratio m:n. Find the values of m and n.

Apparently I wasn't exactly sure of how they meant divide but from where i worked out, the points did not fit on the line AB :/

if they dont fit then it usually means its an external division
use the formula posted above ^

 

[4025808]

Internally or externally?

Regardless you follow this principle

mx +/- nx / m-n = x coodinate.

my +/- ny /m - n = y coodinate.

Simulataneous equations to find m and n if needed

its externally, coz the points don't even fit the lines...
how do you do it externally?
i only know how to do it internally

 

[hscishard]

Oh crap, I was lazy to put +/- on the denom.
I was hoping you guys wouldn't notice.

 

[ohexploitable]

Just sub them values into...



and...



and solve for whatever...

 

[ohexploitable]

Just sub them values into...



and...



and solve for whatever...

 

[4025808]

May you please help me out with these two questions...

10. The point P (11, -28) divided the interval AB in the ratio m:3. If A and B have coordinates (-1, 8) and (2, 1) respectively, find the value of m.

11. The point P (-10, 21) divides the interval AB with coordinates (-2, 5) and (2, -3) in the ratio m:n. Find the values of m and n.

Apparently I wasn't exactly sure of how they meant divide but from where i worked out, the points did not fit on the line AB :/

 

[hscishard]

Internally or externally?

Regardless you follow this principle

mx +/- nx / m-n = x coodinate.

my +/- ny /m - n = y coodinate.

Simulataneous equations to find m and n if needed

 

[4025808]

Just sub them values into...



and...



and solve for whatever...

did that, but I got 2 different values for the value of M

 

[hscishard]

What the hell? This thread is ffed up. The messages aren't in chronological order.

You get two different values of m?! Doubt it. Try it again

 

[4025808]

What the hell? This thread is ffed up. The messages aren't in chronological order.

You get two different values of m?! Doubt it. Try it again

apparently they changed the times right between the first post and the last few because they rewinded the time by one hour...

yeah i did try it
no matter how much i tried it still came with two diff values

 

[hscishard]

K I'll try now. It's better that they rewinded it back. Had to mentally calculate the real time.

 

[hscishard]

For 10, the points aren't even collinear. So it's impossible to work it out. WTF. You sure thats the real question?

 

[hscishard]

For x





For y




Simulatenous equations. You will find they are equal.

wtf?

 

[hscishard]

Using a graphical method. You will find that the distance AP and PB are in 2:1

Since external division is extending it by m then going back by n, we get 2:3

Therefore m=2 and n=3

 

[hscishard]

Aha! I see the flaw when using the forumla.

Sketching is very important here. You will see that We need B to A.

What I did was A to B, which is incorrect.
Therefore since it is B to P then P back to A,

(x2,y2) is (-2,5) and (x1,y1) is (2,-3)

 

[4025808]

Using a graphical method. You will find that the distance AP and PB are in 2:1

Since external division is extending it by m then going back by n, we get 2:3

Therefore m=2 and n=3

yeah i did that but i wasn't sure so i asked you ppl
my answer was right in the first place for Q 11

oh yeah i suppose you'd use distance formula for PA and PB then?

 

[4025808]

For 10, the points aren't even collinear. So it's impossible to work it out. WTF. You sure thats the real question?

yup that is the real question
just typing it off the actual worksheets that the school gave us to do as holiday hwk