Question

draw the graph of x+y=6 which intersects the xaxis and the yaxis at A and B respectively find the length of seg AB also find the area of triangleAOB where O is the point of origin​

Answer 1

Answer:

X=1.5y=6.5

Step-by-step explanation:

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Answer 2

The value of length of segment AB = $6\sqrt{2}$ Unit

The area of the triangle formed is A = 18 $Unit^{2}$

Step-by-step explanation:

Given equation of line x + y = 6 ------- ( 1 )

Put x = 0 in equation ( 1 ) , we get y = 6

⇒ x = 1 , y = 5

⇒ x = 2 , y = 4

⇒ x = 3 , y = 3

⇒ x = 4 , y = 2

⇒ x = 5 , y = 1

⇒ x = 6 , y = 0

Plot the graph between X-Y axis  for the given values of x & y. it is shown in image below.

Now from the graph ,

The area of the triangle formed is given by

⇒ $A = \frac{1}{2} x y$

⇒ A = $\frac{1}{2}$ × 6 × 6

⇒ A = 18 $Unit^{2}$

Now the length of segment AB = $\sqrt{OA^{2} + OB^{2} }$

OA = 6 & OB = 6

⇒ AB = $\sqrt{6^{2} + 6^{2} }$

⇒ AB = $\sqrt{72}$

⇒ AB = $6\sqrt{2}$

This is the value of segment AB.