Q . IF a , b , c FORM AN A.P WITH COMMON DIFFEREN

Question

​Q . IF a , b , c FORM AN A.P WITH COMMON DIFFERENCE ‘d’ ( d not equal to 0) AND x , y , z FORM G.P WITH COMMON RATIO ‘r’( r not equal to 1) , THEN THE AREA OF THE TRIANGLE WITH VERTICES – (a , x) , (b , y) AND (c,z) IS INDEPENDENT OF-( MORE THAN ONE OPTION CAN BE CORRECT)	a	b	x	r

Y RAJYALAKSHMI · Accepted Answer

a, b, c are in AP, ie, b = a + d, c = a + 2d x, y, z are in GP, ie. y = xr, z = xr2 The area of triangle is ½ |a(y – z) + b(z – x) + c(x – y)|Consider a(y – z) + b(z – x) + c(x – y) = a(xr – xr2) + (a + d)(xr2 – x) + (a + 2d)(x – xr)= axr – 2axr + 2axr – ax + dxr2 – dx + ax – axr + 2dx – 2dxr= dxr2 + dx – 2dxr which is independent of a, b, c, y, z

Integral Calculus> Q . IF a , b , c FORM AN A.P WITH COMMON...

Q . IF a , b , c FORM AN A.P WITH COMMON DIFFERENCE ‘d’ ( d not equal to 0) AND x , y , z FORM G.P WITH COMMON RATIO ‘r’( r not equal to 1) , THEN THE AREA OF THE TRIANGLE WITH VERTICES – (a , x) , (b , y) AND (c,z) IS INDEPENDENT OF-( MORE THAN ONE OPTION CAN BE CORRECT)

a

b

x

r

Bharat Makkar , 11 Years ago

Y RAJYALAKSHMI

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Integral Calculus> ​Q . IF a , b , c FORM AN A.P WITH COMMON...

​Q . IF a , b , c FORM AN A.P WITH COMMON DIFFERENCE ‘d’ ( d not equal to 0) AND x , y , z FORM G.P WITH COMMON RATIO ‘r’( r not equal to 1) , THEN THE AREA OF THE TRIANGLE WITH VERTICES – (a , x) , (b , y) AND (c,z) IS INDEPENDENT OF-( MORE THAN ONE OPTION CAN BE CORRECT) a b x r

Bharat Makkar , 11 Years ago

Y RAJYALAKSHMI

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Integral Calculus> Q . IF a , b , c FORM AN A.P WITH COMMON...

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