Question

A(0,0),B(1,2) are two points. If a point P moves such that the area of triangle PAB is 2 square units, then the locus of P is
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Answer 1

Step-by-step explanation:

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Answer 2

Concept:

A triangle is a 2D shape having three sides and three angles and sum of angles is 180°.

Area of triangle =  [ x₁ ( y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)] / 2

Given:

A(0,0),B(1,2) are two points.

Area of triangle PAB is 2 square units.

Find:  

We are asked to seek out the locus of P.

Solution:

Let P = (h, k)

So, points become (0,0), (1,2), (h, k)

And,

Using the above-mentioned formula,

Area of triangle =  [ x₁ ( y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)] / 2

i.e.

2 =  [ 0 ( 2 - k) + 1 (k - 0) + h (0 - 2)] / 2

2 = [ 0 + k - 2h ] / 2

⇒

4 = k - 2h

⇒  k - 2h - 4 = 0

Now, Replace h and k with x and y,

i.e.

y - 2x -4 = 0

So, this is the locus of P.

Hence we can say that the locus of P is y - 2x -4 = 0.

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