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The graph of 3x + 4y – 24 = 0 forms a triangle OAB with the coordinate axes, where O is the origin. Also the graph of x + y+4 =0 forms a triangle OCD with the coordinate axes. Then the area of ∆OCD is equal to
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1 of area of ∆ OAB 2 -
1 of area of ∆ OAB 3 -
2 of area of ∆ OAB 3 - the area of ∆OAB
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Correct Option: B
On putting x = 0 in the equation 3x + 4y = 24
| 4y = 24 ⇒ y = | = 6 | |
| 4 |
∴ Co-ordinates of B = (0, 6)
Again, putting y = 0 in the equation 3x + 4y = 24,
3x = 24 Þ x = 8
∴ Co-ordinates of A = (8,0)
Similarly, for x + y = – 4
Co-ordinates of C = (–4, 0)
Co-ordinates of D = (0, –4)
| ∴ Area of ∆OAB = | × OA × OB = | × 8 × 6 = 24 sq. units | ||
| 2 | 2 |
| Area of ∆OCD = | × OC × OD = | × 4 × 4 = 8 sq. units | ||
| 2 | 2 |
Clearly,
| ∆ OCD ≡ | ∆OAB | |
| 3 |
