Math, asked by cathoora, 3 months ago


6) Find the area of the triangle formed by the line x/a +y/a

= 1 with the coordinate axes.​

Answers

Answered by assingh
43

Topic :-

Coordinate Geometry

Given :-

A line (x/a) + (y/a) = 1

To Find :-

Area of the triangle formed by the given line and coordinate axes.

Solution :-

We will draw the graph of the line and then we will note down the intercepts cut by the line as intercepts will act as base and height of the triangle.

Steps to draw graph of line,

Put x = 0 in the equation of given line.

(x/a) + (y/a) = 1

(0/a) + (y/a) = 1

0 + (y/a) = 1

y = a

Mark point (0, a) on the graph.

Similarly,

Put y = 0 in the equation of given line.

(x/a) + (y/a) = 1

(x/a) + (0/a) = 1

(x/a) + 0 = 1

x = a

Mark point (a, 0) on the graph.

Now, j०in the two marked points to obtain the line.

Observing graph,

After joining the two points we can observe that a line is formed which forms triangle with coordinate axes.

We can also observe that the formed triangle is having base and height equal to 'a units'.

Calculating area of the triangle,

Area = (1/2) × Base × Height

Area = (1/2) × a × a sq. units

(Base = Height = a units )

Area = (a²/2) sq. units

Answer :-

So, the area of given formed triangle is (a²/2) sq. units.

Attachments:
Similar questions