.If the graph of the equation 4x+3y=12 cuts the coordinate axes at A and B then hypotenuse of right triangle AOB is of length
(2 Points)
4 units
3 units
5 units
none of these
Answers
Answer: Triangle formed by line 4x+3y= 12 with coordinate axes.
Therefore we have find the coordinates of A and B.
=>4x+3[o]=12 .......{substitute y=0 because Point A lies on X axes then the u coordinates of the point is 0}
=>x=3 and y = 0
Now, 4[0]+3y=12...{substitute x = 0 because B lies on y axes }
=>y=4 and x =0
Therefore the Point A[3,0] and B [0,4]
The distance between A and B is = rt[(3^) +4^2]
=>rt[25]
=>5 units
Therefore the hypotenuse of AOB is 5 units
Hope the Answer was helpful.
Step-by-step explanation:
Equation is 4x + 3y = 12
If it cuts the x-axis, then y = 0
∴ 4x x 3 x 0 = 12
⇒ 4x = 12 ⇒ x = 12/4 = 3
OA = 3 units
∴ The point of intersection of x-axis is (3, 0)
Again if it cuts the y-axis, then x = 0 , Y= 0
∴ 4x x 3 x 0 = 12
⇒ 4x = 12 ⇒ x = 12/3 = 4
⇒ OB = 4 units
∴ The point of intersection is (0, 4)
∴ In right ΔAOB,
AB2 = AO2 + OB2
= (3)2 + (4)2
= 9 + 16 = 25
= (5)2
∴ AB = 5 units