Invariant Points

Q. When I opened the brackets then all sign will changed or not?

Q.

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper.

(iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA'BB'.

(v) Name two invariant points under reflection in the x-axis.

Q.

P and Q have co-ordinates (0, 5) and (-2, 4).

(a) P is invariant when reflected in an axis. Name the axis.

(b) Find the image of Q on reflection in the axis found in (a)

(c) (0, k) on reflection in the origin is invariant. Write the value of k.

(d) Write the co-ordinates of the image of Q, obtained by reflection it in the origin followed by reflection in x-axis.

Q.

Match the following:

$\begin{array}{cccc}& Point& & Invariantwithrespecttoline\\ a.& (-3,2)& \left(i\right)& y=4\\ b.& (2,-3)& \left(ii\right)& x=4\\ c.& (-1,4)& \left(iii\right)& y=2\\ d.& (4,-1)& \left(iv\right)& x=2\end{array}$

1. a(ii), b(i), c(iii), d(iv)

2. a(iii), b(ii), c(i), d(iv)

3. a(i), b(iii), c(ii), d(iv)

4. a(iii), b(iv), c(i), d(ii)

Q.

Points A (-8, 0), B (-16, 0) are invariant points when reflected in the line $L_1$ . Find the image of the points C (-15, 6) and D(8, 19) in the line $L_1$.

1. (-15, -6), (8, 19)

2. (-15, -6) , (-8, 19)

3. (15, 6) , (-8, 19)

4. (-15, -6) , (-8, -19)

Q. Points $(-5,0)$ and $(4,0)$ are invariant points under reflection in the line $L_1$; points $(0,-6)$ and $(0,5)$ are invariant on reflection in the line $L_2$.
(a) Name or write equations for the lines $L_1$ and $L_2$.
(b) Write down the images of $P(2,6)$ and $Q(-8,-3)$ on reflection in $L_1$. Name the images as $P^{\prime }$ and $Q^{\prime }$ respectively.
(c) Write down the images of $P$ and $Q$ on reflection in $L_2$. Name the images as $P^{\prime \prime }$ and $Q^{\prime \prime }$ respectively.
(d) State or describe a single transformation that maps $Q^{\prime }$ onto $Q^{\prime \prime }$.

Q.

A point P is its own image under the reflection in a line l. Describe the position of the point P with respect to the line l.

Q. Which of the following points will be invariant under reflection in the x axis?

1. (0, 1)
2. ( -1, 1)
3. (-1, 0)
4. (1, 1)

Q.

The point is its own image if the point is __

Q. Let R be the relation on the set R of all real numbers defined by a R b if $|a-b|\le \frac{1}{2}$. Then R is?

1. Reflexive and symmetric but not transitive
2. Transitive but neither reflexive nor symmetric
3. Reflexive, symmetric and transitive
4. Symmetric and transitive but not reflexive

Q.

$(-13,0)$ is an invariant point under the reflection in the x-axis. State whether true or false.

1. False

2. True

Q.

Point (0, 5) is an invariant point when reflected in _____

1. X - axis

2. Y - axis

3. Origin(0, 0)

4. None othe above

Q.

$(-13,0)$ is an invariant point when reflected in the x-axis. State whether true or false.

1. True

2. False

Q.

Reflection of $(0,-12)$ in the y-axes is ___________

1. (0, 12)

2. (0, 2)

3. (0, -12)

4. (0, 0)

Q. Points (-5, 0) and (4, 0) are invariant points under reflection in the y-axis.

1. False
2. True

Q.

The invariant point under reflection in the x-axis, y-axis and origin is ________________

1. (0, 1)

2. (1, 1)

3. (0, 0)

4. (1, 0)

Q.

Reflection of $(-12,0)$ in the x-axis is ___________

1. (-12, 0)

2. (0, 12)

3. (-12, 12)

4. (2, 12)

Q.

The Point (4, 0) is an invariant point when reflected in _____

1. X-axis

2. Origin(0, 0)

3. Y-axis

4. None of the above

Q. The point (-3, 0) on reflection in a line is mapped as (3, 0) and the point (2, -3) on reflection in the same line is mapped as (-2, -3).
(i) Name the mirror line.
(ii) Write the co-ordinates of the image of (-3, -4) in the mirror line.

Q.

If the image of a point P is P itself, then P is an ___ point.