1.Two points A(10, -4) and B (-2 ,8) are given.Point P(1,5) divides AB internally in the ratio of r : 1.Find the value of r.
write down your process please=)
ABOUT Coordinate
2007-05-05 12:16 am
回答 (3)
2007-05-05 12:28 am
✔ 最佳答案
from the question, AP:PB=r:1therefore, consider x-coordinate of P, i.e.1,
1=(10*1+(-2)*r)/r+1
r+1=10-2r
3r=9
r=3
alternate method,
consider y-coordinate of P, i.e. 5
5=((-4)*1+8*r)/r+1
5r+5=8r-4
-3r=-9
r=3
no matter which method you use, you will get the SAME answer.
2007-05-05 1:29 am
use section formula
Let m : n = r : 1 ,coordinates of P are (X,Y) ,coordinates of A are (X1,Y1) ,coordinates of B are (X2,Y2)
X = (nX1 + mX2) / (m + n)
Y = (nY1 + mY2) / (m + n)
the x-coordinate of P
↓
1 = [1 x (10) + r x (-2)] / r+1
r + 1 = 10 + (-2r) ←cross mutiplcation
r + 1 = 10 - 2r
3r = 9
r = 3
Let m : n = r : 1 ,coordinates of P are (X,Y) ,coordinates of A are (X1,Y1) ,coordinates of B are (X2,Y2)
X = (nX1 + mX2) / (m + n)
Y = (nY1 + mY2) / (m + n)
the x-coordinate of P
↓
1 = [1 x (10) + r x (-2)] / r+1
r + 1 = 10 + (-2r) ←cross mutiplcation
r + 1 = 10 - 2r
3r = 9
r = 3
參考: me , section formula
2007-05-05 12:32 am
[10*1)+(-2*R)]/(1+R)=1
10-2R=1+R
9=3R
R=3
10-2R=1+R
9=3R
R=3
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