1.

Plot the points A(1,5) B(-1,1) andC(4,1) name the figure so obtained Find it’s area

Answer»

Given :

  • Coordinates of B = ( -1 , 1 )

  • Coordinates of C = ( 4 , 1 )

To FIND :

  • Area of triangle ABC

Solution :

Area of triangle is

\boxed{ \boxed{ \sf \purple{Area = \dfrac{1}{2} \bigg[ x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 -y_2) \bigg] }}}

Here

\sf x_1 = 1 \: \: \: \: \: \: \: \: \: \: x_2 = - 1 \: \: \: \: \: \: \: \: x_3 = 4 \\ \\ \sf y_1 =5 \: \: \: \: \: \: \: \: \: \: y_2 = 1 \: \: \: \: \: \: \: \: \: \: \: \: y_3 = 1

Substitute values in formula

\sf \implies \dfrac{1}{2} \bigg[ 1(1 - 1) - 1(1 - 5) + 4(5 - 1) \bigg] \\ \\\sf \implies \dfrac{1}{2} \bigg[ 1(0) - 1( -4) + 4(4) \bigg] \\ \\ \sf \implies \dfrac{1}{2} \bigg[0 + 4 + 16 \bigg] \\ \\ \sf \implies \frac{1}{2} \times 20 \\ \\\sf \implies10

\Large \underline {\sf \green{Area \: of \: triangle = 10 \: {unit}^{2}}}


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