Question

find the locus of points P(x, y) which moves so that the area of the triangle with vertices formed by the points P1(3, 5), P2(5, 8) and P has an area of 10 square units.

Answer 1

then A = 0.5*b*h

Answer 2

you have to use distance formulae

Answer 3

yeah figure that much, i'm just confused with the area thing >,<

Answer 4

use area equation to get an equation interms of x and y

Answer 5

should i assume that the base should be the two given points?

Answer 6

\[10=0.5\times b\times h
\]
yes. from the diagram, for that fixed base, the height is fixed too.

Answer 7

you'd get a number for b
\[h^2={25\over b^2}\]
equate the two H62 equations.

Answer 8

ok i'll try it thanks

Answer 9

um where did you get the 25?

Answer 10

do you know a little about determinants?

Answer 11

you can also use Heron's formula as follows:
\[
4A^2=|P_1P_2|^2|P_1P|^2-(P_1P_2-P_1P)^2
\]

Answer 12

sorry i don't know anything about determinants or i don't remember it, sorry

Answer 13

sorry. (10/0.5)^2=400
mistake..

Answer 14

not 25

Answer 15

oh its ok, your helping afterall, i don't have the right to complain^_^

Answer 16

yes determinants..
\[
A = {1\over2}\left|\begin{matrix}x_0&y_0&1\\x_1&y_1&1\\x_2&y_2&1\end{matrix}\right|
\]

Answer 17

way easier this way

Answer 18

so,
\[
2\times10=\left|\begin{matrix}
x&y&1\\
3&5&1\\
5&8&1
\end{matrix}\right|
\]

Answer 19

oh that, so i'll just plug the points in there then copy the first two columns or not?

Answer 20

you have to expand the determinant now

Answer 21

ok try to figure out how to expand determinants, thanks