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)

line is  

y - y₁ = [(y₂ - y₁) / (x₂ - x₁)]*(x - x₁)

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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