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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.. TODAY 2 SEPT 2010SAUMYA

## 1 Answers

10 years ago

Q.1 Let the coordinates of B be (x1, y1) and that of C be (x2, y2). Therefore the mid point of BC is

(x1 + x2) /2 = 5 and (y1 + y2) /2 = 6 so, x= 10 - x2 & y1 = 12 - y2. But B(x1, y1) satisfies

2x + 3y = 29 & C(x2, y2) satisfies x + 2y = 16 therefore, 2x1 + 3y1 = 29__(i) & x2 + 2y2 = 16__(ii)

Putting the value of x1 & y1 in the first equation 7 then by simplifying we get, 2x2 + 3y2 = 27__(iii)

Now solving equation (ii) & (iii) we get, y2 = 3 and x2 = 10 so, equation passing through (5, 6) &
(10, 3) i.e BC is (x - 5) / (y - 6) = (5 - 10) / (6 - 3) i.e 3x + 5y = 45.

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