Question

Find the area
of a triangle having vertices (3, 2), (9,-1) and (5,7).​

Answer 1

Answer:

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Answer 2

Given:

A triangle has vertices (3, 2), (9,-1) and (5,7).​

To Find:

Find the area

Solution:

A triangle is a 2-dimensional figure with 3 sides and has 3 angles. The sum of the 3 angles of a triangle is equal to 360 degrees.

Now to find the area of a triangle with the coordinates of the vertices as (x1,y1), (x2,y2) and (x3,y3) we will use the formula as,

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

Now the given coordinates of the triangle are,

(3, 2), (9,-1) and (5,7).

So using the formula for the area of a triangle in coordinate geometry is,

$Area=\frac{1}{2} |[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|\\\\=\frac{1}{2} |[3(-1-7)+9(7-2)+5(2+1)]|\\\\=\frac{1}{2}|[-24+45+15]|\\\\ =\frac{1}{2} *36\\\\=18 unit^2$

Hence, the area of the triangle is 18 sq. units.