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141.
Find values of k if area of triangle is 4 sq. units and vertices are (k, 0), (4, 0), (0, 2).

Since area of the triangle formed by the points (k, &), (4, 0), (0, 2) is 4 sq. units

therefore space space space space space space space 1 half open vertical bar table row straight k cell space space 0 end cell cell space space 1 end cell row 4 cell space 0 end cell cell space space 1 end cell row 0 cell space space 2 end cell cell space space 1 end cell end table close vertical bar space equals space plus-or-minus 4 space space space space space space space space space space space space space space space rightwards double arrow space space space space space space space space space space open vertical bar table row straight k cell space space 0 end cell cell space space 1 end cell row 4 cell space space 0 end cell cell space space space 1 end cell row 0 cell space space 2 end cell cell space space space 1 end cell end table close vertical bar space equals space plus-or-minus 8 therefore space space space space space space minus 2 space open vertical bar table row straight k cell space space 1 end cell row 4 cell space space 1 end cell end table close vertical bar space equals space plus-or-minus 8 space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space minus 2 left parenthesis straight k minus 4 right parenthesis space equals space plus-or-minus 8 therefore space space space space space minus 2 space straight k space plus space 8 space equals space 8 comma space space minus 8 space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space minus 2 space straight k space equals space 0 comma space space minus 16 therefore space space space space space space space space space straight k space equals space 0 comma space space 8 space space space space space space space space space space

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142.

Find values of k if area of triangle is 4 sq. units and vertices are (– 2, 0), (0, 4), (0, k)

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143. Find the equation of the line joining A(l, 3) and B(0, 0) using determinants and find k if D(A, 0) is a point such that area of triangle ABD is 3 sq. units.

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144.

Find equation of line joining (1, 2) and (3, 6) using determinants.

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145.

Find equation of line joining (3, 1) and (9, 3) using determinants.

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Long Answer Type

146. A triangle has its three sides equal to a, b and c. If the coordinates of its vertices are A(x₁ y₁), B(x₂, y₂) and C(x₃ y₃), show that

space open vertical bar table row cell straight x subscript 1 end cell cell space space straight y subscript 1 end cell cell space 2 end cell row cell straight x subscript 2 end cell cell space straight y subscript 2 end cell cell space 2 end cell row cell straight x subscript 3 end cell cell space straight y subscript 3 end cell cell space 2 end cell end table close vertical bar squared space equals space left parenthesis straight a plus straight b plus straight c right parenthesis thin space left parenthesis straight b plus straight c minus straight a right parenthesis thin space left parenthesis straight c plus straight a minus straight b right parenthesis thin space left parenthesis straight a plus straight b minus straight c right parenthesis.

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Multiple Choice Questions

147. If area of triangle is 35 sq. units with vertices (2, – 6), (5, 4) and (k, 4). Then k is

12
-2
-12, -2
-12, -2

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Short Answer Type

148.

Find the minor of element 6 in the determinant $increment space equals space open vertical bar table row 1 cell space 2 end cell cell space 3 end cell row 4 cell space 5 end cell cell space 6 end cell row 7 cell space 8 end cell cell space 9 end cell end table close vertical bar$

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149.

Find the minors and co-factors of the elements a₁₁, a₂₁ in the determinant.

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150.

Find minors and cofactors of all the elements of the determinant:
$open vertical bar table row 1 cell space space minus 2 end cell row 4 cell space space space 3 end cell end table close vertical bar$ .