Question

The area
of the triangle with vertices at (-4,1), (1, 2) (4, -3) is​

Answer 1

Answer:

The area of the triangle is 14 sq. units.

Step-by-step explanation:

In coordinate geometry, we learnt that given the coordinates of the vertices of a triangle, we can find its area using this formula:

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

Taking (-4,1) to be the first vertex, (1,2) to be the second vertex and (4,-3) to be the third, we can find the area by inserting the values into the formula:

$A=|\frac{1}{2} \{-4[2-(-3)]+1(-3-1)+4(1-2)\}|\\\\=|\frac{1}{2} [-4(2+3)+1(-4)+4(-1)]|\\\\=|\frac{1}{2} [-4(5)-4-4]|\\\\=|\frac{1}{2} (-20-8)|\\\\=|\frac{1}{2} *(-28)|\\\\=|-14|\\=14$

So, the area of the triangle is 14 sq. units.

Hope it helps!

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