Question

The area of the triangle formed by the co-ordinates axes and a line is 6 sq. units and
the length of the hypotenuse is 5 units. Find the equations of the line.


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Answer 1

Hello there,,,,, here is your solution

The equation of the line with intercepts a and b is .

The line intersects the axes at A (a, 0) and B (0, b).

Let O be the origin.

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

... (1)

Here, the length of the hypotenuse is 5 units, i.e. AB =5

... (2)

Let us find the possible values of a and b from (1) and (2).

Using equation (1)

Now, from equation (1)

For

For

Hence, the possible equations of the lines are

, , ,

or 4x + 3y = 12 or 4x 3y = 12 or 4x + 3y = 12 or 4x 3y = 12 or 3x + 4y = 12 or x 4y = 12 or 3x + 4y = 12 or 3x 4y = 12

Hope this helps you

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