Question

graph the following. A(4,1) B(1,5)C(-2,1)draw a triangle ABC and find its area​

Answer 1

Given:

Coordinates of  point A = (4,1)

Coordinates of point  B =(1,5)

Coordinates of point C = (-2,1)

These three points A , B and C are making a triangle .

To Find :

Area of this triangle and its graph with given points = ?

Solution :

The graph of this triangle is shown in the attached fig .

Now the area of this triangle is given as :

$area\triangle ABC = \frac{1}{2}\left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{array}\right|$

                   $=\frac{1}{2}\left|\begin{array}{ccc}4&1&1\\1&5&1\\-2&1&1\end{array}\right|$

                  =$\frac{1}{2} [4(5-1) -1{1-(-1)}+1(1-(-10)]$

                  =$\frac{1}{2}(4 \times 4 -3 + 11)$

                  =$\frac{1}{2}\times 24 = 12$

Hence , the area of this triangle ABC is 12 sq. units .

Answer 2

Thr above answer is correct