Question

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Answer 1

Step-by-step explanation:

Given :-

x = y and x+2y = 3

To find :-

Draw the graph of the lines x=y and x+2y=3 also find the area bounded by these lines and x-axis ?

Solution :-

See the above attachment for graph

Scale :-

On X-axis 1 cm = 1 unit

On Y-axis 1 cm = 1 unut

For x = y we get the points (0,0),(1,1),(2,2),..

The graph of the line x = y is a straight line which passes through the origin.

For x+2y = 3 we get the points ( (0,3/2),(1,1),(3,0),(-3,3)...

The graph of the line is a straight line

The region enclosed by the points O(0,0) , A(3,0) and B(3/2,0) is shaded.

∆ABC is formed

Area of a triangle = (1/2) base × height sq.units

We have,

Base = OA = 3 units

Height = OB = 3/2 units

Area of OAB = (1/2)×(3)×(3/2)

=> Area of ∆OAB = (3/2)×(3/2)

=>Area of ∆OAB = 9/4 sq.units = 2.25 sq.units

(Or)

Let (x1, y1) = O(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = A(3,0) => x2 = 3 and y2 = 0

Let (x3, y3) = B(0,3/2) => x3 = 0 and y3 = 3/2

We know that

Area of a triangle formed by the points (x1, y1) , (x2, y2) and (x3, y3) is given by

∆=(1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

On Substituting these values in the above formula then

=>∆=(1/2) | 0(0-3/2)+3{(3/2)-0}+0(0-0) |

=>∆ = (1/2) |0+(9/2)+0 |

=> ∆ = (1/2)(9/2)

=> ∆ = 9/4 sq.units

=> ∆ = 2.25 sq.units

Answer:-

The area of a triangle formed by the given lines is 2.25 sq.units

Used formulae:-

• Area of a triangle formed by the points (x1, y1) , (x2, y2) and (x3, y3) is given by
• ∆=(1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units
• Area of a triangle = (1/2) base × height sq.units
• The equation of x-axis is y=0
• The equation of y-axis is x = 0