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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the area of this triangle is
Solution
Let vertex be $A(1,2)$.Midpoints of sides through $A$ are:
$M_1(-1,1)$ and $M_2(2,3)$
Let other two vertices be $B(x_1,y_1)$ and $C(x_2,y_2)$.
Using midpoint formula:
$\left(\frac{1+x_1}{2},\frac{2+y_1}{2}\right)=(-1,1)$
$x_1=-3,\ y_1=0$
So, $B(-3,0)$
Similarly,
$\left(\frac{1+x_2}{2},\frac{2+y_2}{2}\right)=(2,3)$
$x_2=3,\ y_2=4$
So, $C(3,4)$
Area of triangle:
$\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$
$=\frac{1}{2}|1(0-4)+(-3)(4-2)+3(2-0)|$
$=\frac{1}{2}|-4-6+6|$
$=\frac{1}{2}\times 4$
$=2$
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