Question

find the area of the triangle formed by the points (2,3),(3,-1),(-4,2)​

Answer 1

★given:-

• triangle formed by the points (2,3),(3,-1),(-4,2)

★find:-

• area of the triangle

★solution:-

• we know that triangle area find formula

$\implies ar\triangle = \star \pink{ \frac{1}{2} | x_{1}( y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3}( y_{1} - y_{2}) | }$

• when we comparison points (2,3),(3,-1),(-4,2)

$\implies \red{ x_{1} = 2 } \: \: \: \: \implies\blue{ y_{1} = 3} \\ \\ \\ : \implies\red{ x_{2} = 3} \: \: \: \: \implies \: \blue{y_{2} = - 1} \\ \\ \\ \implies \: \red{ x_{3} = - 4} \: \: \: \: \implies \blue{ y_{3} = 2 }$

we use triangle formula

$\implies \frac{1}{2} |2( - 1 - 2) + 3(2 - 3) + ( - 4)(3 - ( - 1)| \\ \\ \\ \implies \: \frac{1}{2} |2( -3 ) + 3( - 1) - 4(3 + 1)| \\ \\ \\ \implies \frac{1}{2} | - 6 - 3 - 4(4)| \\ \\ \\ \implies \: \frac{1}{2} | - 6 - 3 - 16| \\ \\ \\ \implies \frac{1}{2} | - 25| \\ \\ \\ \implies \: \frac{1}{2} \times 25 \\ \\ \\ \implies \red{12.5}$

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$\implies \: area \triangle = \star \pink {12.5 }\: \: unit$

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I hope it helps you