Question

Find the area of the triangle whose vertices are (2,3),(5,-6) and (-7,10).​

Answer 1

The area of the triangle whose vertices are (2,3),(5,-6) and (-7,10).​ is 30 square units

Step-by-step explanation:

We know that area of the triangle whose vertices are $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ is given by

$A=\frac{1}{2}|[x_1(y_2-x_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|$

Given the coordinate of the vertices of the triangle

$(2,3), (5,-6),(-7,10)$

Therefore, the area is

$A=\frac{1}{2}|[2(-6-10)+5(10-3)+(-7)(3-(-6))]|$

$\implies A=\frac{1}{2}|[2(-16)+5(7)+(-7)(9)]|$

$\implies A=\frac{1}{2}|[-32+35-63]|$

$\implies A=\frac{1}{2}|[-60]|$

$\implies A=30$ square units

Hope this answer is helpful.

Know More:

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Answer 2

Given :

The coordinates of the three vertices are (2,3) , (5,-6) and (-7,10) .​

To find :

The area of the triangles formed by the given vertices .

Solution :

The area of the triangle formed by vertices (x1 , y1) , (x2 , y2) and (x3 , y3) is

area Δ  = 0.5* | [x1 * ( y2 - x3 ) + x2 * ( y3 - y1 ) + x3 * ( y1 - y2 ) ] |

area of the given triangle = 0.5 * | [ 2 * ( -6 - 10 ) + 5 * ( 10 - 3 ) + (-7) * ( 3 - (-6) ) ] |

                                           = 0.5 * | [ 2 * ( -16 ) + 5 * ( 7 ) + ( -7 ) * 9 ] |

                                           = 0.5 * | [ -32 + 35 - 63 ] |

                                           = 0.5 * 60

                                           = 30

The area of the triangles formed by the given vertices is 30 square units .