Question

Area of Triangle with point (1,2) (3,6) (5,10) is

• A. 0
• B. 2
• C. 4
• D. 6

Hint:

Before calculating the full area, check if the points follow a linear pattern. Here, for every increase of 2 in $x$, $y$ increases by 4 ($y = 2x$). Since all points satisfy this, they are collinear and the area is 0.

Answer 1

The Correct Option is A

Step 1: Form the two vectors from the first point to the other two: \(\vec{AB} = (3-1, 6-2) = (2,4)\) and \(\vec{AC} = (5-1, 10-2) = (4,8)\).

Step 2: Check if one vector is a scalar multiple of the other: \((4,8) = 2 \times (2,4)\), so \(\vec{AC} = 2\vec{AB}\).

Step 3: Since \(\vec{AC}\) is a scalar multiple of \(\vec{AB}\), all three points lie on the same straight line, meaning they are collinear and enclose no actual area.
\[ \text{Area} = \boxed{0} \]