The co-ordinates of the centroid of a Δ ABC are (1, -4

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 Multiple Choice QuestionsMultiple Choice Questions

11.

The graph of the linear equation 3x + 4y = 24 is a straight line intersecting x-axis and y-axis at the points A and B respectively. P(2, 0) and  are two points on the sides OA and OB respectively of Δ OAB, where O is the origin of co-ordinate system. Given that AB = 10 cm, then PQ = 

  • 20 cm

  • 2.5 cm

  • 40 cm

  • 40 cm

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12.

The area of a triangle with vertices A(0, 8), O(0, 0) and B (5, 0) is

  • 8 sq units

  • 13 sq units

  • 20 sq units

  • 40 sq units

146 Views

13.

If the distance between two points (0, -5) and (x, 0) is 13 unit, then x equal to

  • 10

  • plus-or-minus space 10

  • 12

  • plus-or-minus space 12

80 Views

14.

The area of the triangle formed by the lines 5x + 7y = 35,   4x + 3y = 12 and x-axis is

  • 160/13 sq units

  • 150/13 sq units

  • 140/13 sq units

  • 10 sq units

82 Views

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15.

The distance between the points (0, 0) and the intersecting point of the graph of x = 3 and y = 4 is

  • 3 units

  • 2 units

  • 5 units

  • 4 units

60 Views

16.

A triangle is formed by the x-axis and the lines 2x + y  = 4 and x - y + 1 = 0 as three sides. Taking the side along x-axis as its base, the corresponding altitude of the triangle is

  • 3 units

  • √5 units

  • 1 units

  • 2 units

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17.

An equation of the form ax + by + c = 0, where, straight a not equal to 0 comma space space straight b not equal to 0 space space and space straight c space equals space 0 represents a straight line which passes through

  • (2, 4)

  • (0, 0)

  • (3, 2)

  • None of these

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18.

ax + 5y = 8 has slope of negative 4 over 3. What is the value of a?

  • 20 over 3

  • 3 over 20

  • negative 20 over 3

  • negative 3 over 20


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19.

The co-ordinates of the centroid of a Δ ABC are (1, -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3, -4) and (0, 5) respectively.

  • (0, 13)

  • (0, 5)

  • (0, -5)

  • (0, -13)


D.

(0, -13)

Let the co-ordinates of vertex c be (x, y).
x1 = 3,    y1 = -4,    x2 = 0,   y2 = 5,      x3 = x,  y3 = y
According to the question,
rightwards double arrow space space space space open parentheses fraction numerator straight x subscript 1 space plus space straight x subscript 2 space plus space straight x subscript 3 over denominator 3 end fraction comma space space space space space space space fraction numerator straight y subscript 1 space plus space straight y subscript 2 space plus space straight y subscript 3 over denominator 3 end fraction close parentheses space equals space left parenthesis 1 comma space minus space 4 right parenthesis
rightwards double arrow space space space space open parentheses fraction numerator 3 space plus space 0 space plus space straight x over denominator 3 end fraction space equals space 1 comma space space space space space space space fraction numerator negative 4 space plus space 5 space plus space straight y over denominator 3 end fraction space equals space minus 4 close parentheses
rightwards double arrow space space space 3 space plus space straight x space equals space 3 space comma space space space space 1 space plus space straight y space equals space minus 12
rightwards double arrow space space space space space straight x space equals space 0 comma space space space space space space space space space space straight y space equals space minus 13 space space
Point C(0,  -13)


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20.

What is the reflection of the point (-1, 3), in the line x = -4?

  • (-7, -3)

  • (-7, 3)

  • (7, -3)

  • (7, 3)


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