Math, asked by aramesh1507, 2 months ago

Find the area
of the triangle whose
vertices are (2,3) (-1,10) and (2,-4)​

Answers

Answered by assingh
19

Topic :-

Coordinate Geometry

Given :-

There is a triangle with vertices (2, 3), (-1, 10) and (2, -4).

To Find :-

Area of the given triangle.

Formula to be Used :-

Area of a triangle when coordinates of the triangle are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by :-

\Delta=\dfrac{1}{2}\left | x_1y_2-x_2y_1+x_2y_3-x_3y_2+x_3y_1-x_1y_3\right |

\Delta\;refers\:to\:area\:of\:the\:triangle.

Solution :-

(2,3) \equiv (x_1,y_1)

(-1,10) \equiv (x_2,y_2)

(2,-4) \equiv (x_3,y_3)

Applying formula,

\Delta=\dfrac{1}{2}\left |(2)(10)-(-1)(3)+(-1)(-4)-(2)(10)+(2)(3)-(2)(-4)\right |

\Delta=\dfrac{1}{2}\left |20-(-3)+4-20+6-(-8)\right |

\Delta=\dfrac{1}{2}\left |20+3+4-20+6+8\right |

\Delta=\dfrac{1}{2}\left |41-20\right |

\Delta=\dfrac{1}{2}\left |21\right |

\Delta=\dfrac{21}{2}

\Delta=10.5\;\;sq.\:units

Answer :-

So, area of the given triangle is 10.5 square units.

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