Question

The area of triangle ABC whose vertices areA(-2,4),B(2,-6) and C(5,4) is

Answer 1

Given: A triangle ABC formed by the points A(-2, 4), B(2, -6) and C(5, 4).

To find: The area.

Answer:

Formula to find the area of a triangle:

$\tt Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(x_1\Big(y_2\ -\ y_3\Big)\ +\ x_2\Big(y_3\ -\ y_1\Big)\ +\ x_3\Big(y_1\ -\ y_2\Big)\Bigg)$

From the points, we have:

$\tt x_1\ =\ -2\\\\x_2\ =\ 2\\\\x_3\ =\ 5\\\\y_1\ =\ 4\\\\y_2\ =\ -6\\\\y_3\ =\ 4$

Using them in the formula,

$\tt Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(-2\Big(-6\ +\ 4\Big)\ +\ 2\Big(4\ -\ 4\Big)\ +\ 5\Big(4\ +\ 6\Big)\Bigg)\\\\\\Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(-2\Big(-2\Big)\ +\ 2\Big(0\Big)\ +\ 5\Big(10\Big)\Bigg)\\\\\\Area\ =\ \dfrac{1}{2}\ \times\ \Bigg(4\ +\ 0\ +\ 50\Bigg)\\\\\\Area\ =\ \dfrac{1}{2}\ \times\ 54\\\\\\\bf Area\ =\ 27\ units$

Therefore, the area of the triangle formed by the points A(-2, 4), B(2, -6) and C(5, 4) is 27 units.