Question

if P(x,y) is any point on the line segment joining A(a,0) and B(0,b) show that x/a+y/b=1​

Answer 1

Answer:

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Answer 2

When three points are collinear then area of triangle is equal to zero

Step-by-step explanation:

Given: P(x,y) is any point on the line segment joining A(a,0) and B(0,b)

To prove: $\dfrac{x}{a}+ \dfrac{y}{b} =1$

As P(x,y) lies on the line segment joining  A(a,0) and B(0,b)

therefore A , B , P are collinear

Therefore as we know area of triangle

$area= \dfrac{1}{2} (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))$

Let

$(x_1,y_1) =P(x,y), (x_2,y_2) =A(a,0), (x_3,y_3) =B(0,b)$

Now substituting the values

$0= \dfrac{1}{2} (x(0-b)+a(b-y)+0(y-0))\\\\\Rightarrow 0= -xb+ab-ay\\\\\Rightarrow ab=xb+ay$

dividing the whole equation by ab we get

$\Rightarrow \dfrac{ab}{ab}= \dfrac{xb}{ab} +\dfrac{ay}{ab} \\\\\Rightarrow 1= \dfrac{x}{a} +\dfrac{y}{b}$

Hence,proved the required result

#Learn more

Find the area of triangle whose coordinates are (1,2),(3,4) and (5,10)

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