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131. If a, b, c are in A.P, then the determinant

open vertical bar table row cell straight x plus 2 end cell cell space space space straight x plus 3 end cell cell space space space straight x plus 2 straight a end cell row cell straight x plus 3 end cell cell space space straight x plus 4 end cell cell space space straight x plus 2 straight b end cell row cell straight x plus 4 end cell cell space space straight x plus 5 end cell cell space space space straight x plus 2 straight c end cell end table close vertical bar

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132. Find the area of the triangle with vertices (2, 7), (1, 1), (10, 8).

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133.

Find the area of the triangle, whose vertices are (3, 1), (4, 3) and (-5, 4).

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134.

Find the area of the triangle with vertices at the points given in each of the following:
(1, 0) (6,0), (4, 3)

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135.

Find the area of the triangle with vertices at the points given in each of the following:
(2, 7), (1, 1), (10, 8)

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136.

Find the area of the triangle with vertices at the points given in each of the following:
(–2,–3), (3, 2), (–1,–8)

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137.

Show that points A(a, b + c), B(b, c + a), C(c, a + b) are collinear.

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Let ∆ be the area of the triangle whose vertices are (11, 7), (5, 5), (– 1, 3).

therefore space space increment space equals space 1 half open vertical bar table row 11 cell space space 7 end cell cell space space 1 end cell row 5 cell space space 5 end cell cell space space 1 end cell row cell negative 1 end cell cell space space 3 end cell cell space space 1 end cell end table close vertical bar space space space equals space 1 half open vertical bar table row 11 cell space space space space 7 end cell cell space space space space 1 end cell row cell negative 6 end cell cell space minus 2 end cell cell space space space space 0 end cell row cell negative 12 end cell cell space minus 4 end cell cell space space space space 0 end cell end table close vertical bar comma space space straight R subscript 2 space minus straight R subscript 1 comma space space straight R subscript 3 space minus straight R subscript 1 space space space space space equals space 1 half open vertical bar table row cell negative 6 end cell cell space space space minus 2 end cell row cell negative 12 end cell cell space space space minus 4 end cell end table close vertical bar space equals space 1 half left parenthesis 24 minus 24 right parenthesis space equals space 0. therefore space space space given space points space left parenthesis 11 comma space 7 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis space and space left parenthesis negative 1 comma space 3 right parenthesis space are space collinear. space space space space space

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139.

Determine x so that the points (3, 2), (x, 2) and (8, 8) lie on a line.

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140. Find the value of x if the area of triangle is 35 square cm. with vertices (x, 4), (2, – 6) and (5, 4).

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