Mathematics
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.
Coordinate Geometry
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Answer
Vertex B lies in the fourth quadrant. The square's sides are along the coordinate axes, so one vertex, O, is at the origin (0, 0).
The side length is 4 units.
With O at (0, 0), the other two vertices on the axes must be A (4, 0) on the positive x-axis and C (0, -4) on the negative y-axis.
The fourth quadrant is where the x-coordinates are positive and the y-coordinates are negative.
Vertex B is located at the point where the line extending 4 units to the right from C (0, -4) intersects with the line extending 4 units down from A (4, 0), which is (4, -4).
⇒ B = (4, –4).
∴ Statement 1 is true, and statement 2 is false.
Hence, option 3 is the correct option.
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Related Questions
Three vertices of a square ABCD are A(2, 0), B(-3, 0) and C(-3, -5). Its fourth vertex D is:
(2, 5)
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