Question

In the $xy$-plane, the vertices of a triangle are $(-1,3),(6,3)$ and $(-1,-4)$. The area of the triangle is ___ square units.

• A. $10$
• B. $17.5$
• C. $24.5$
• D. $35$

Answer 1

The correct option is C $24.5$

If $(x_1,y_1)$,$(x_2,y_2)$ and $(x_3,y_3)$ are the vertices of a triangle then its area is given by,

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

Therefore, with the vertices $(-1,3)$, $(6,3)$ and $(-1,-4)$.

Area of triangle is given by,

$A=\left|\frac{1}{2}\right(-1(3-(-4\left)\right)+6(-4-3)+(-1)(3-3)\left)\right|$

$=\left|\frac{1}{2}\right(-7-42\left)\right|$

$=\left|\frac{1}{2}\right(-49\left)\right|$

$=|-24.5|$

$=24.5$ square units.