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Introduction to Symmetry

If a shape is...

Question

If a shape is symmetric, then it will be symmetric about all lines passing through its centre.

A

False

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B

True

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Solution

The correct option is A False

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Q. If y = f(x) is symmetric about the lines 3x + 4y + 1 = 0 and 4x – 3y – 7 = 0, then it must be symmetric about

Q. If a given matrix is symmetric, diagonal or triangular, then its adjoint matrix will also be symmetric, diagonal or triangular respectively.

Q. Identify the true statements in the following :
(i) If a curve is symmetrical about the origin, then it is symmetrical about both the axes.
(ii) If a curve is symmetrical about both the axes, then it is symmetrical about the origin.
(iii) A curve

f (x, y) = 0

is symmetrical about the line

y = x

f (x, y) = f (y, x)

.
(iv) For the curve

f (x, y) = 0

f (x, y) = f (- y, - x)

then it is symmetrical about the origin.

Q. Question 6 (a)
(a) Copy the diagram and complete each shape to be symmetric about the mirror line (s):

Q. Assertion :The curve

y = \frac{- x^{2}}{2} + x + 1

is symmetric with respect to the line

x = 1

. Reason: A parabola is symmetric about its axis.

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