Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION

Find the area of the triangle ABC with A(1,-4) and the mid-points of sides through A being (2,-1) and (0,-1)

EXPLANATION
Explain TypeExplanation Content
Text

Let the Coordinates of B and C be (a,b) and (x,y), respectively.

Then, $\left ( \frac{1+a}{2},\frac{-4+b}{2} \right )=(2,-1)$

Therefore,    1+a=4, -4+b=-2

a=3, b=2

Also, $\left ( \frac{1+x}{2},\frac{-4+y}{2} \right )=(0,-1)$

Therefore, 1+x=0,-4+y=-2

i.e.,             x=-1 i.e., y=2

The coordinate of the vertices of $\Delta ABC$ are A(1,-4), B(3,2) and C(-1,2)

Area of $\Delta ABC=\frac{1}{2}[1(2-2)+3(2+4)-1(-4-2)]$

$=\frac{1}{2}[18+6]=12$sq. units

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