Straight LineHardBloom L3
Question
The ends of the base of an isosceles triangle are at $(2,0)$ and $(0,1)$ and the equation of one side is $x = 2$ then the orthocentre of the triangle is:
Options
A.$\left( \frac{3}{4},\frac{3}{2} \right)$
B.$\left( \frac{5}{4},1 \right)$
C.$\left( \frac{3}{4},1 \right)$
D.$\left( \frac{4}{3},\frac{7}{12} \right)$
Solution
Sol. [Key Concept: Isosceles triangle with base ends and side $x = 2$: apex on the perpendicular bisector, then the orthocentre.]
Slope of HD = 2
$$\Rightarrow \ \frac{1 - \frac{1}{2}}{\lambda - 1} = 2 \Rightarrow \lambda = \frac{5}{4}$$
$$\therefore\ H \equiv \left( \frac{5}{4},1 \right)$$
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