If (a, b), (c, d) and (e, f) are the vertices of △ABC and △ ...

CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 10 of 20

Marks: +1, -0

If (a, b), (c, d) and (e, f) are the vertices of △ABC and △ denotes the area of △ABC, then

{|\table a, c, e\b,d,f;1,1,1|}^2

is equal to:

Solution:

Area of the triangle with vertices (a, b), (c, d) and (e, f) is given by:

\;{12}/{|\table a,b,1; c,d,1\e,f,1|}=△

⇒ {|\table a,b,1; c, d ,1; e, f,1|}=2△

Now,

{|\table a,b,1; c, d ,1; e, f,1|}={|\table a, c,e; b, d , f;1,1,1|}

( ∵ | A^T | = | A | )

∴ {|\table a,c,e; b,d,f; 1,1, 1|}=4△ ^2

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