In a triangle ABC- A- - B-2-3- C-1-3 and point A lies on line y-2x-3 where - I- Area of triangle ABC- - is such that -5- Possible coordinates of A are where - represents greatest integer function

The correct option is C ( 5, 7) Area of triangle, =12 #160;α amp; β amp; 1 2 amp; 3 amp; 1 1 amp; 3 amp; 1 R_1→ R_1 ...

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Byju's Answer

Standard VII

Mathematics

Area Method to Find Condition for Co-Linearity

In a triangle...

Question

In a triangle $A B C$ , $A = (α, β), B = (2, 3), C = (1, 3)$ and point $A$ lies on line $y = 2 x + 3$ where $α, β \in I$ . Area of triangle $△ A B C$ , $Δ$ is such that $[Δ] = 5$ . Possible coordinates of $A$ are (where $[.]$ represents greatest integer function)

(2, 3)

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(5, 13)

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(- 5, - 7)

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(- 3, - 5)

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Solution

The correct option is C $(- 5, - 7)$
Area of triangle, $△ = \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} α & β & 1 2 & 3 & 1 1 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$
$R_{1} \to R_{1} - R_{3}$ and $R_{2} \to R_{2} - R_{3} △ = \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} α - 1 & β - 3 & 0 1 & 0 & 0 1 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$
Expanding along $C_{3}, △ = \frac{1}{2} (3 - β)$ As $β \in I [△] = 5 \Rightarrow △ = 5$ or $△ = 5.5 \Rightarrow β = - 7$ or $- 8,$ BUt $β = - 8$ gives $α = - 5.5 \times (α \in I) \Rightarrow β = - 7$ and $α = - 5 =$

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In a triangle ABC, A=(α,β),B=(2,3),C=(1,3) and point A lies on line y=2x+3 where α,β∈I. Area of triangle △ABC, Δ is such that [Δ]=5. Possible coordinates of A are (where [.] represents greatest integer function)

In a triangle $A B C$ , $A = (α, β), B = (2, 3), C = (1, 3)$ and point $A$ lies on line $y = 2 x + 3$ where $α, β \in I$ . Area of triangle $△ A B C$ , $Δ$ is such that $[Δ] = 5$ . Possible coordinates of $A$ are (where $[.]$ represents greatest integer function)