Coordinate geometry

• May 2nd 2010, 11:41 PM
Punch
Coordinate geometry
Given a straight line BD where point E lies on it.

Coordinates $B(0.5,3)$ and $E(1,1)$

Find the coordinates of D given that $BE : ED = 1:3$ and the equation of the line BD is $y=-4x+5$
• May 3rd 2010, 03:18 AM
Soroban
Hello, Punch!

Was that the original wording of the problem?

Quote:

Given points $B\left(\tfrac{1}{2},\:3\right)$ and $E(1,\:1)$

Find the coordinates of point D so that $BE : ED = 1:3$

Here's a back-door approach . . .

Code:

              ½       B(½,3)o - +             \  :             d \ : 2               \:           E(1,1)o - - - +                 \      :                   \    :                   \    :                 3d \  :                     \  :                       \ :                       \:                       D o

Going from $B$ to $E$, we moved $\tfrac{1}{2}$ unit right and 2 units down.
. . And we moved a diagonal distance $d.$

Going from $E$ to $D$, we want to move a diagonal distance $3d.$
. . Hence, we must triple our previous moves.

From $E$, we move ${\color{blue}\tfrac{3}{2}}$ units right and 6 units down.

Therefore, point $D$ is: . $\left(\tfrac{5}{2},\;\text{-}5\right)$

• May 3rd 2010, 05:42 AM
mrmohamed
Quote:

Originally Posted by Soroban
Hello, Punch!

Was that the original wording of the problem?

Here's a back-door approach . . .

Code:

              ½       B(½,3)o - +             \  :             d \ : 2               \:           E(1,1)o - - - +                 \      :                   \    :                   \    :                 3d \  :                     \  :                       \ :                       \:                       D o
Going from $B$ to $E$, we moved $\tfrac{1}{2}$ unit right and 2 units down.
. . And we moved a diagonal distance $d.$

Going from $E$ to $D$, we want to move a diagonal distance $3d.$
. . Hence, we must triple our previous moves.

From $E$, we move ${\color{blue}\tfrac{3}{2}}$ units right and 6 units down.

Therefore, point $D$ is: . $\left(\tfrac{5}{2},\;\text{-}5\right)$

HI all
Excuse me Mr soroban
what about Point D (-1/2 , 7 )????
in my solution I found D(5/2 , -5 ) and D(-1/2 , 7 )
mrmohamed
• May 3rd 2010, 06:49 AM
Punch
Quote:

Originally Posted by Soroban
Hello, Punch!

Was that the original wording of the problem?

Here's a back-door approach . . .

Code:

              ½       B(½,3)o - +             \  :             d \ : 2               \:           E(1,1)o - - - +                 \      :                   \    :                   \    :                 3d \  :                     \  :                       \ :                       \:                       D o
Going from $B$ to $E$, we moved $\tfrac{1}{2}$ unit right and 2 units down.
. . And we moved a diagonal distance $d.$

Going from $E$ to $D$, we want to move a diagonal distance $3d.$
. . Hence, we must triple our previous moves.

From $E$, we move ${\color{blue}\tfrac{3}{2}}$ units right and 6 units down.

Therefore, point $D$ is: . $\left(\tfrac{5}{2},\;\text{-}5\right)$

Hi! its you again :) I have understood your workings and I knew this before I asked this question on MHF. However, I am still a little puzzled on how to present my workings...
• May 3rd 2010, 07:13 AM
Soroban
Hello, mrmohamed!

Quote:

What about Point D (-1/2 , 7 )?

That point is also correct . . . Good work!

Silly me . . . I assumed directed distances,

. . as in . $\overrightarrow{BE} : \overrightarrow{ED} \:=\:1:3$

• May 3rd 2010, 07:47 AM
mrmohamed
Quote:

Originally Posted by Punch
Given a straight line BD where point E lies on it.

Coordinates $B(0.5,3)$ and $E(1,1)$

Find the coordinates of D given that $BE : ED = 1:3$ and the equation of the line BD is $y=-4x+5$

HI all
http://i69.servimg.com/u/f69/12/89/99/77/almonk12.jpg
with my best wishes
mrmohamed
• May 4th 2010, 04:31 AM
Punch
Thanks! but in the solution sheet shows only point is: $\left(\tfrac{5}{2},\;\text{-}5\right)$ and the marks allocated to this question is probably only 2-3... judging from the long workings, perhaps your working is a more elaborated one compared to what is required of me?