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Coordinate Geometry

Sponsor Area

Question
SSCCGLENQA12042705
Wired Faculty App

Area of the triangle formed by the graph of the straight lines x - y = 0,  x + y = 2 and x-axis is 

  • 1 sq unit

  • 2 sq units

  • 1 sq units

  • None of these

Solution

A.

1 sq unit

On putting x = 0 in 
x + y = 2,
0 + y = 2  ⟹  y = 2
∴  Point of intersection on y-axis   (0, 2)
Again, putting y = 0 in  x + y = 2, ⟹  x = 2
∴  Point of intersection on x-axis  = (2, 0)
x - y = 0 will pass through origin and be equally inclined to axes.

On putting x = y  in   x + y = 2,
2y = 2  ⟹ y = 1
∴  CD = 1
  OA = 2
Area of ΔOAC = 1 half cross times OA cross times CD
      equals space 1 half space cross times space 2 space cross times space 1 space equals space 1 space sq. space unit


Sponsor Area

Question
SSCCGLENQA12042557
Wired Faculty App

If the ordinate and abscissa of the point (k,  2k -1) be equal, then the value of k is

  • 0

  • -1

  • 1

  • 1 half

Solution

C.

1

Abscissa = k,
ordinate = 2k - 1
According to the question,
  rightwards double arrow space space straight k space equals space 2 straight k space minus space 1 rightwards double arrow space space 2 straight k space minus straight k space equals space 1 space rightwards double arrow space space straight k space equals space 1

Question
SSCCGLENQA12042555
Wired Faculty App

The area (in square units) of the triangle formed by the graphs of the equations x = 4,  y = 3 and 3x + 4y = 12 is

  • 24

  • 12

  • 6

  • 3

Solution

C.

6

On putting x = 0 in the equation 3x + 4y = 12,
4y = 12,  ⟹  y = 3
Again on putting y = 0,
3x = 12   ⟹  x = 4

∴ Area of ΔABC = 1 half cross times AC cross times BC
   equals space 1 half cross times 3 cross times 4 space equals space 6 space square space units.

Question
SSCCGLENQA12042218
Wired Faculty App

The area of the triangle formed by the graphs of the equations x = 4, y = 3 and 3x + 4y = 12 is

  • 4 sq units

  • 12 sq units

  • 6 sq units

  • 3 sq units

Solution

C.

6 sq units


therefore  Required area of AOB = 1 half cross times 3 cross times 4 space equals space 6 space sq space units.

Question
SSCCGLENQA12043016
Wired Faculty App

The area of the triangle formed by the straight line 3x + 2y = 6 and the co-ordinate axes is

  • 3 square units

  • 6 square units

  • 4 square units

  • 8 square units

Solution

A.

3 square units

Putting y = 0 in the equation 3x + 2y = 6
3x + 0 = 6 ⟹ x = 2

∴   Point of intersection on x-axis =  (2, 0)
Putting x = 0, in the equation
   3x + 2y = 6
    0 + 2y = 6
⟹    y = 3
∴   Point of intersection on y-axis = (0, 3)
∴    OA = 2,   OB = 3
therefore space increment OAB space equals space 1 half cross times space OA space cross times space OB space equals space 1 half cross times space 2 space cross times space 3 space equals space 3 space sq. space units
   
 

Sponsor Area

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