Question

Find the area of triangle with vertices 1,3 ( 1,7) and 8,4
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Answer 1

Given :

• Coordinates of triangle = A ( 1 , 3 )

• Coordinates of triangle = B ( 1 , 7 )

• Coordinates of triangle = A ( 8 , 4 )

To Find :

• Area of the triangle

Solution :

$\large \sf Area_{triangle} = \dfrac{1}{2} \bigg[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \bigg]$

Here

$\sf x_1 = 1 \: \: \: \: \: \: \: \: \:x_2 = 1 \: \: \: \: \: \: \: \: \:x_3= 8 \\ \\ \sf y_1 = 3 \: \: \: \: \: \: \: \: \:y_2 = 7 \: \: \: \: \: \: \: \: \:y_3= 4$

Substitute values in formula

$\implies \sf area = \frac{1}{2} \bigg[1(7 - 4) + 1(4 - 3) + 8(3 - 7) \bigg] \\ \\\implies \sf Area = \frac{1}{2} \bigg[1(3) + 1(1) + 8( - 4) \bigg] \\ \\\implies \sf Area = \frac{1}{2} \bigg[3 +1 - 32 \bigg]\\ \\\implies \sf Area = \frac{1}{2} \times - ( 28 ) \\ \\ \large\implies \boxed{ \sf \purple{ Area = - 14 \: {unit}^{2}}}$