Question

If the vertices of a triangle are (2,4), (5,k) and (3,10) and its area is 15 sq. units, the value of k is

• A. $-8$
• B. $10$
• C. $-12$
• D. $\frac{23}{2}$

Answer 1

The correct option is C $-12$

Area of the triangle $=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

here$x_1=2,y_1=4$

$x_2=5,y_2=k$

$x_3=3,y_3=10$

Area of the triangle=15 sq.units

$15=\frac{1}{2}\left[2\right(k-10)+5(10-4)+3(4-k\left)\right]$

$15=\frac{1}{2}[2k-20+30+12-3k]$

$30=22-k$

$k=22-30$

$k=-8$