Question

Draw the graph of x + y = 6 which intersects the X-axis and the Y-axis

at A and B respectively. Find the length of seg AB. Also, find the area

of ∆ AOB where point O is the origin.

Answer 1

Answer:

length of seg AB is 6√2 unit

area of ΔAOB is 18 sq. unit

Step-by-step explanation:

The line x+y=6 intersects x-axis at (a,0). Substituting this in the equation we have a=6.

Similarly, The line x+y=6 intersects x-axis at (0,b). Substituting this in the equation we have b=6

∴ The line intersects x and y axes at A(6,0) and B(0,6).

The length of the line joining points (x₁,y₁) and (x₂,y₂) is given by the distance formula,

$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

So, the length of AB = $\sqrt{(0-6)^{2}+(6-0)^{2}} = 6 \sqrt{2}$

Area of triangle = (1/2) * Base * Height

ΔAOB is right angled with OA as base and OB as height.

The lengths of OA and OB are 6 units each.

∴Area of ΔAOB = (1/2) * 6 *6 = 18 sq. units

Hence,

length of seg AB is 6√2 unit and

area of ΔAOB is 18 sq. unit