Let the area of the triangle with vertices A 1 , α , B α , 0 and C 0 , α be 4 sq. units. If the points α , - α , - α , α and α 2 , β are collinear, then β is equal to

Question

Let the area of the triangle with vertices A 1 , &#945; , B &#945; , 0 and C 0 , &#945; be 4 sq. units. If the points &#945; , - &#945; , - &#945; , &#945; and &#945; 2 , &#946; are collinear, then &#946; is equal to

Aicharya · Accepted Answer

Given, the area of the triangle with vertices

A (1, α), B (α, 0)

and

C (0, α)

be

4

sq. units

Now applying formula for area we get,

$\frac{1}{2} |\begin{array}{l} α & 0 & 1 \\ 1 & α & 1 \\ 0 & α & 1 \end{array}| = \pm 4$

$\Rightarrow α = \pm 8$

Now given points will be $(8, - 8), (- 8, 8), (64, β)$

OR $(- 8, 8), (8, - 8), (64, β)$

Given above points are collinear, so their slope will be equal, so $slope= \frac{8 + 8}{- 8 - 8} = - 1$

$\Rightarrow \frac{β - 8}{64 + 8} = - 1$

$\Rightarrow β = - 64$

Let the area of the triangle with vertices A 1 , α , B α , 0 and C 0 , α be 4 sq. units. If…

Solution

Let the area of the triangle with vertices A 1 , &#945; , B &#945; , 0 and C 0 , &#945; be 4 sq. units. If…

Solution

Let the area of the triangle with vertices A 1 , α , B α , 0 and C 0 , α be 4 sq. units. If…