Question

Draw the graph of the following equation name the triangle find its coordinate and area
x=0; y=0; x-2y-3=0​

Answer 1

Answer:

Right-angled triangle

(0, 0), (0, -3/2) and (3, 0)

9/4 unit^2

Step-by-step explanation:

Notice that x = 0 and y = 0 represent y-axis and x-axis respectively, which are perpendicular to each other. Hence the triangle so formed must be a right-angled triangle.

x = 0 and y = 0 meet at (0, 0).

x = 0 and x - 2y - 3 = 0 meet at (0, -3/2)

y = 0 and x - 2y - 3 = 0 meet at (3, 0)

*using substitution, values are given

Using the formula for area in coordinate geometry is tough, relating to just 1/2 bh.

Using distance formula,

1st leg = √(0 - 3)² + (0 - 0)² = 3

2nd leg = √(0 - 0)² + (0 + 3/2)² = 3/2

Hence,

Area of ∆ = 1/2 (3)(3/2) = 9/4 unit^2

Answer 2

Given :-

x - 2y - 3 = 0

To Find :-

Coordinate

Solution :-

x - 2y - 3 = 0

x - 2y = 0 + 3

x - 2y = 3

Putting x as 0

0 - 2y = 3

- 2y = 3

y = -3/2

Coordinates = (0,-3/2)

Putting y = 0

x - 2(0) = 3

x - 0 = 3

x = 3

Coordinate (3,0)

Now

Area = 1/2 × base × height

Area = 1/2 × 3 × 3/2

Area = 9/4

Area = 2.25 cm²