Question

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

Answer 1

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.