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Raksha

· started a discussion

· 1 Months ago

doubt (Question:586503.0)

equation 2 kaise aayi formula ,m rakhne pr mera 9 nhi aaya

Question:

The area of a triangle is 4.5 square units. The two vertices of triangle are (3,2) and (4, -5). The third vertex lies on y = x- 2. Find the third vetex.

Options:
A)

(4, 2)

B)

3 , 6

C)

(1, 3 )

D)

(2, 0) or  174, 94   

Solution:

Ans: (d)

Area of triangle formed by the points (3, 2) and (4, - 5) and (x1, y1) =  12    [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)] 

=  12x1-5-2+4 2- y1+3 y1+5   

=  12- 7 x1, +8-4y, +3y1+15   

=  12- 7 x1, - y1+23   

∵ (x1 , y1) lies on the lines y = x – 2 

∴ y1 = x1 – 2 ________________(1)

From the given condition, it is obvious that,

± 12-7 x1- y1+23=4.5   

⇒ -7x1 – y1 + 23 = 9 

⇒ -7x1 – y1 + 14) = 0 _________(2) 

Or, - (-7x1 – y1 + 23) = 9

⇒ 7x1 + y1, - 23 = 9

⇒ 7x1 + y1,  = 32 __________(3) 

By solving (1) & (2) we get

X1 = 2 and y1 = 0

By Solving (1) and (3) we get

x1= 174, y1= 94    

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