Algebra
- What is the area of the region bounded by straight line 9x + 4y = 36, x - axis and the y - axis ?
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Putting y = 0 in 9x + 4y = 36 9x = 36 ⇒ x = 4
∴ Co-ordinates of point A = (4, 0)
i.e OA = 4 units
Putting x = 0 in 9x + 4y = 36
4y = 36 ⇒ y = 9
∴ Co-ordinates of point B = (0, 9)
i.e. OB = 9 units∴ Area of ∴OAB = 1 × OA × OB 2 Correct Option: B
Putting y = 0 in 9x + 4y = 36 9x = 36 ⇒ x = 4
∴ Co-ordinates of point A = (4, 0)
i.e OA = 4 units
Putting x = 0 in 9x + 4y = 36
4y = 36 ⇒ y = 9
∴ Co-ordinates of point B = (0, 9)
i.e. OB = 9 units∴ Area of ∴OAB = 1 × OA × OB 2
- The slope of the given line is:
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Slope = tan XAB
∵ 90° < ∠XAB < 180°
∴ The slope will be negative because tanθ is negative in second quadrant.= 1 × 4 × 9 = 18 sq.units 2 Correct Option: B
Slope = tan XAB
∵ 90° < ∠XAB < 180°
∴ The slope will be negative because tanθ is negative in second quadrant.= 1 × 4 × 9 = 18 sq.units 2
- What is the area of the triangle formed by points (0,0), (3,4), (4,3) ?
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(x1, y1) = 0, 0, ( x2, y2) = (3, 4), (x3, y3) = (4, 3)Area of ∆OAB = x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) 2 = 0(4 - 3) + 3(3 - 0) + 4(0 - 4) 2 = 9 - 16 = 7 sq. units 2 2 Correct Option: B
(x1, y1) = 0, 0, ( x2, y2) = (3, 4), (x3, y3) = (4, 3)Area of ∆OAB = x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) 2 = 0(4 - 3) + 3(3 - 0) + 4(0 - 4) 2 = 9 - 16 = 7 sq. units 2 2
- The area of a triangle with vertices A (0, 8) , O (0,0) and B (5, 0) is :
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Clearly, OA = 5 units
OB = 8 units∴ Area of ∆OAB = 1 × OA × OB = 1 × 5 × 8 = 20 sq.units 2 2 Correct Option: C
Clearly, OA = 5 units
OB = 8 units∴ Area of ∆OAB = 1 × OA × OB = 1 × 5 × 8 = 20 sq.units 2 2
- What is the equation of the line whose y-intercept is (–3/4) and making an angle of 45° with the positive x–axis?
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Slope of straight line = m = tanq = tan45° = 1Intercept on Y–axis = c = - 3 4
∴ The required equation is : y = mx + c⇒ y = 1.x – 3 4
⇒ 4y = 4x – 3
⇒ 4x – 4y = 3Correct Option: A
Slope of straight line = m = tanq = tan45° = 1Intercept on Y–axis = c = - 3 4
∴ The required equation is : y = mx + c⇒ y = 1.x – 3 4
⇒ 4y = 4x – 3
⇒ 4x – 4y = 3