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The Orthocentre

If the point ...

Question

If the point $(0, β)$ lies on or inside the triangle formed by the lines $y = 0$ , $x + y = 8$ and $3 x - 4 y + 12 = 0$ , then $β$ cannot be equal to

A

2

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B

4

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C

8

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D

12

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Solution

The correct options are
B $4$
C $8$
D $12$
For the point $(0, β)$ to be on or inside the triangle
$(i) β \geq 0$
$(i i) β - 8 \leq 0 \Rightarrow β \leq 8$
$(i i i) - 4 β + 12 \geq 0 \Rightarrow β \leq 3$
$\Rightarrow 0 \leq β \leq 3$

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