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1. IN A TRIANGLE ABC EQUATION OF SIDES AB & AC ARE 2x +3y=29 & x + 2y=16. if the midpoint of BC is (5,6) find equation of BC ? 2.AD, BE CF ARE THE ALTITUDES OF TRI. ABC WITH A(-4,5) D(3.2, -4.6) E(4,1) F(-1,-4). FIND EQUATION OF SIDES OF TRI. ABC & COORDINATES OF B & C? SIR PLZ REPLY..
1. IN A TRIANGLE ABC EQUATION OF SIDES AB & AC ARE 2x +3y=29 &
x + 2y=16.
if the midpoint of BC is (5,6) find equation of BC ?
2.AD, BE CF ARE THE ALTITUDES OF TRI. ABC WITH A(-4,5) D(3.2,
-4.6) E(4,1) F(-1,-4).
FIND EQUATION OF SIDES OF TRI. ABC & COORDINATES OF B & C?
SIR PLZ REPLY..
1) say C=(a,b)
C has to satisfy AC eqn
use this for AC equation we get a+2b=16.....................1
and we know BC's mid point is (5,6)
say D=(5,6)
now use the equation of line which passes through two points. here our two points are C(a,b) and D(5,6)
line is
y - y1 = [(y2 - y1) / (x2 - x1)]*(x - x1)
y - 6 = [(b - 6) / (a - 5)] * (x - 5)
this line has to pass throghu B(c,d) we get
c - 6 = [(b - 6) / (a - 5)] * (d - 5)...........................2
again use it for B(c,d) and D(5,6)
using AB equation u will get 2c+3d=32.............3
again use the equation of line which passes through two points. here our two points are B(c,d) and D(5,6)
y - 6 = [(d - 6) / (c - 5)] * (x - 5)
this line has to pass throghu C(a,b) we get
a - 6 = [(d - 6) / (c - 5)] * (b - 5)...........................4
now 4 equations 4 unknowns solve them and get the points B and D..after use two point line formula again we get the equations
2)
use same line rules and equation mentioned above u will get this answer too. do practice and solve second one so that u will remember it
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