Find the area of the triangle with vertices at the points given

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 Multiple Choice QuestionsMultiple Choice Questions

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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 Multiple Choice QuestionsShort Answer Type

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) 


Let ∆ be the area of the triangle whose vertices are (1,0), (6, 0), (4,3).
therefore space space space space space space space increment space equals space 1 half open vertical bar table row 1 cell space space 0 end cell cell space space 1 end cell row 6 cell space 0 end cell cell space space 1 end cell row 4 cell space 3 end cell cell space space 1 end cell end table close vertical bar space equals space 1 half open square brackets 1 space open vertical bar table row 0 cell space space space 1 end cell row 3 cell space space space space 1 end cell end table close vertical bar plus 1 space open vertical bar table row 6 cell space space space 0 end cell row 4 cell space space space space 3 end cell end table close vertical bar close square brackets
space space space space space space space space space space space space space space space space equals space 1 half open square brackets 1 left parenthesis 0 minus 3 right parenthesis plus 1 space left parenthesis 18 minus 0 right parenthesis close square brackets space equals space 1 half left parenthesis negative 3 plus 18 right parenthesis space equals space 15 over 2 space equals space 7.5 space sq. space units.
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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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138.

Using determinants, show that the points (11, 7), (5, 5) and (– 1, 3) are collinear.

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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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