Question

Represent the following equations graphically. x – y = 0, x + y = 0, y + 5 = 0. Also, find the area enclosed between these lines.

Answer 1

First let us take the equation 1.

$x - y = 0 \\ = > x = y$

This means that the value of x and y will be the same in this equation.

If. x=1 , y=1

x=0 , y=0

Hence we get 2 coordinates for eq. 1. i.e.

A (1, 1) and B (0, 0).

Now similarly for equation 2.

$x + y = 0 \\ = > x = (- y)$

Now in this case, the face value for x and y would remain the same, but the sign would change.

So, if x=0 , y= 0

x=1, y= -1

Again we get 2 coordinates for eq. 2 i.e.

C (0, 0) and D (1, -1).

For the eq. 3

we are given

$y + 5 = 0 \\ = > y = ( - 5)$

In this case, for any value of x, the coordinate for y would always remain -5

Hence the eq. can also be written as

$0x + y = ( - 5)$

So, if x=0 , y= (-5)

, y= (-5) x= 1 , y= (-5)

we get 2 coordinates for eq. 2 i.e.

E (0, -5) and F (1, -5).

You will have to count the boxes between the points M and N to get the length of the base and between A and E to get the height or altitude of the triangle.

Ar(AMN) =

$= \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 10 \times 5 \\ = 5 \times 5 \\ = 25 \: sq. \: cm.$