Mathematics
Statement 1: In the given diagram, OAB is an equilateral triangle.
Co-ordinates of the vertex B = (4, 4)
Statement 2: B = (4, )
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Coordinate Geometry
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Answer
Given equilateral triangle OAB.
OA = OB = AB = 8 units.
Draw BD ⊥ OA.
In an equilateral triangle, a perpendicular drawn from one of the vertices to the opposite side bisects the side.
∴ OD = x OA = x 8 = 4.
In right angle triangle OBD,
By pythagoras theorem,
⇒ OB2 = OD2 + BD2
⇒ 82 = 42 + BD2
⇒ 64 = 16 + BD2
⇒ BD2 = 64 - 16
⇒ BD2 = 48
⇒ BD =
⇒ BD =
From graph,
Co-ordinates of O = (0, 0)
Co-ordinates of A = (8, 0)
As, OD = 4 units and BD = units.
Co-ordinates of B = (4, ).
∴ Statement 1 is false, and statement 2 is true.
Hence, option 4 is the correct option.
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Related Questions
A point lies on y-axis at a distance of 2 unit from x-axis. Its co-ordinates are :
(2, 0) only
(0, 2) only
(2, 2)
(0, 2) or (0, -2)
Three vertices of a square ABCD are A(2, 0), B(-3, 0) and C(-3, -5). Its fourth vertex D is:
(2, 5)
(2, -5)
(-2, 5)
(-2, -5)
Statement 1: The vertex B of square OABC with each side 4 units lies in the fourth quadrant and its side are along the co-ordinate axes. The co-ordinate of vertex B are (4, -4).
Statement 2: B = (4, 4)
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A): PQR is an equilateral triangle. The co-ordinates of point Q are (0, ).
Reason (R): In ΔOPQ,
OQ2 = PQ2 - OP2 = 42 - 22 = 12.
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.