Question

The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line

Answer 1

It is given that ,The area of the triangle formed by the coordinate axes and a line is 6 square units .

We get any one of two right angled triangles shown above :

case 1:

The line intersects x - axis at A( a,0 )= (3,0) and

y - axis at B(0,b) = (0,4)

X - intercept = a = 3 ,

y - intercept = b = 4,

$\underline { \pink { Two \: intercept \:form : }}$

$\boxed { \orange { \frac{x}{a} + \frac{y}{b} = 1 }}$

$Substituting \: the \: values , we \: get \\Equation \: of \:the \:line :$

$\frac{x}{3} + \frac{y}{4} = 1\: ---(1)$

case 2:

The line intersects x - axis at P( a,0 )= (4,0) and

y - axis at Q(0,b) = (0,3)

X - intercept = a = 4 ,

y - intercept = b = 3,

$Substituting \: the \: values , we \: get \\Equation \: of \:the \:line :$

$\frac{x}{4} + \frac{y}{3} = 1\: ---(2)$

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