Area of the triangle formed by the points (−2, 1), (−3, 2) and (−4, 3) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0 sq. units
The area of a triangle with vertices \((x_1, y_1), (x_2, y_2), (x_3, y_3)\) is the absolute value of
\( \displaystyle \Delta = \frac{1}{2}\begin{vmatrix}x_1 & y_1 & 1\\x_2 & y_2 & 1\\x_3 & y_3 & 1\end{vmatrix} \)
\( \displaystyle = \frac{1}{2}\begin{vmatrix}-2 & 1 & 1\\-3 & 2 & 1\\-4 & 3 & 1\end{vmatrix} \)
Expanding along the first row:
\( \displaystyle = \frac{1}{2}\left[-2(2 - 3) - 1(-3 + 4) + 1(-9 + 8)\right] \)
\( \displaystyle = \frac{1}{2}\left[2 - 1 - 1\right] = 0 \)
The area is 0 because the three points are collinear: each step from one point to the next goes 1 left and 1 up, so they lie on one line (y = −x − 1).