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 if p(x,y ) is any point on the line segment joining the points A(a , 0) and B(0,b) then show that x/a + y/b = 1

 Using area of triangle formula , 

1/2 {x1 (y2 - y3) + x2 ( y3 - y1) + x3 ( y1 - y2)}

1/2 { a ( y - b ) + x ( b - 0 ) + 0 ( 0 - y ) }

1/2 { ay - ab + xb }

Since all the points are in a straight line i.e. collinear they cannot form a triangle . 

1/2 { ay - ab + xb } = 0 

ay - ab + xb = 0

- ab + bx = - ay

 - b ( a - x ) = -ay

a - x = - ay / - b

a - x / a = - y/-b

a/a - x/a = -y/-b

1 - x/a = -y / -b

1 = x/a + y/b

(or)

x/a + y/b = 1 

Proved

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See lakhmir singh
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after using the area of triangle formula simply divide the whole equation by ab
 
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See the solution in the picture

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Budbak 😜😜😜😜ho tum log
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Let the ratio in which P(x,y) divides AB be k:1 x=a+0/k+1 y=0+bk/k+1

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Hope this helps.
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see lakhmir singh class 10
 
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its easy
 
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answers 
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Solution

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Please see answer below
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If the point p (x,y)is equidistant from the points A (5,1)and B (-1,5),prove that 3x=2y.
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Please find this answer

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Please find this answer

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Salman Khan man
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Using area of triangle formula ,

1/2 {x1 (y2 - y3) + x2 ( y3 - y1) + x3 ( y1 - y2)}

1/2 { a ( y - b ) + x ( b - 0 ) + 0 ( 0 - y ) }

1/2 { ay - ab + xb }

Since all the points are in a straight line i.e. collinear they cannot form a triangle .

1/2 { ay - ab + xb } = 0

ay - ab + xb = 0

- ab + bx = - ay

- b ( a - x ) = -ay

a - x = - ay / - b

a - x / a = - y/-b

a/a - x/a = -y/-b

1 - x/a = -y / -b

1 = x/a + y/b

(or)

x/a + y/b = 1

Proved
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