Straight LineHardBloom L3
Question
The line $x = c$ cuts the triangle with corners $(0,0),(1,1)$ and $(9,1)$ into two regions. For the area of the two regions to be the same $c$ must be equal to :
Options
A.$5/2$
B.3
C.$7/2$
D.3 or 15
Solution
Sol. [Key Concept: A vertical line $x = c$ splits the triangle; equate the right sub-triangle's area to half the total via similar triangles ⇒ $c = 3$.]
$$\begin{matrix} & 2 \times \frac{1}{2}\left( 1 - \frac{c}{9} \right)(9 - c) = \frac{1}{2} \times 8 \times 1 \\ & \ \Rightarrow \ c = 3 \end{matrix}$$
or $c = 15$ which is not possible
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