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saumya shivhare Grade: 11
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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?
```
7 years ago

## Answers : (1)

69 Points
```										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

```
7 years ago
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