Image of a Point with Respect to Y = a

Q.

The image of a point P on reflection in a Line listen p'. Describe the location of the line l and explain the answer.

Q.

What is the reflection of the point $A(-2,3)$ in the line $y=2$?

1. (-2, -1)

2. (-2, 1)

3. (3, 1)

4. (-2, -3)

Q.

The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P', the imae of P and Q', the image of Q.

Q.

State the co-ordinates of the following points under reflection in x-axis :

(i) (3, 2) (ii) (-5, 4) (ii) (0, 0)

Q.

A line segment has endpoints at $(–1,4)$ and $(4,1)$.

Which reflection will produce an image with endpoints at $(–4,1)$ and $(–1,–4)$?

1. a reflection of the line segment across the x-axis

2. a reflection of the line segment across the y-axis

3. a reflection of the line segment across the line $y=x$

4. a reflection of the line segment across the line $y=–x$

Q.

P(3, 3), Q(7, 6) and R(3, 6) are the coordinates of a triangle. A, B and C are the reflection points of P, Q and R respectively about Y = 0. The area of the triangle formed by the points B, C and D(3, -9) is ___.

Q. The triangle $A(1,2),B(4,4)$ and $C(3,7)$ is first reflected in the line $y=0$ onto triangle $A^{\prime }{B}^{\prime }{C}^{\prime }$ and then triangle $A^{\prime }{B}^{\prime }{C}^{\prime }$ is reflected in the origin onto triangle $A^{\prime \prime }{B}^{\prime \prime }{C}^{\prime \prime }$. Write down the co-ordinates of :
(i) $A^{\prime },B^{\prime }$ and $C^{\prime }$
(ii) $A^{\prime \prime },B^{\prime \prime }$ and $C^{\prime \prime }$.
(2 Marks)

Q. P(3, 3), Q(7, 6) and R(3, 6) are the coordinates of a triangle. A, B and C are the reflection points of P, Q and R respectively about Y = 0.What is the area of the triangle formed by the points B, C and D(3, -9)?

1. 5
2. 6
3. 9
4. 12

Q.

The point (4, 1) and (- 2, 4) are reflected in the line y = 3. Find the coordinates of their images.

1. $(-4,-1),(2,-4)$

2. $(-4,1),(-2,2)$

3. $(4,5),(-2,-2)$

4. $(4,5),(-2,2)$

Q. Find the perpendicular distance of $(2,-3)$ from $y$-axis.

Q. Complete the following table:
Point Transformation Image
$(4,2)$ Reflection in x-axis ........

Q.

Reflection of the point (4, 6) in the line Y+2 = 0 is

1. (4, -4)

2. (4, -8)

3. (4, -6)

4. (4, -10)

Q. The image of a point P (2, 3) under reflection in the origin is P'(x, y). Write down the values of x and y.$\left[3Marks\right]$

Q. The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Then what will be the co-ordinates of P', the imae of P and Q', the image of Q?

1. $$(4,5);(-2,2)$$
2. $$(4,-1);(-2,2)$$
3. $$(4,-1);(2,-4)$$
4. $$(4,-1);(2,-2)$$

Q. If P is (-3, 4) and My Mx (P) shows the reflection of the point P in the x"axis and then the reflection of the image in the y"axis, then My Mx (P) is

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

Q. Point P(-9, 0) is first reflected in y-axis and then reflected in x-axis to obtain P'. The co-ordinates of P' are (-9, 0)

1. True
2. False

Q. Complete the following table:
Point Transformation Image
$(4,-8)$ ...............$(-4,-8)$

Q.

The reflection of point A(-6, 10) about Y = 2 is (c, d). The value of c+d is ___.

1. (6, -10)

2. (-6, -10)

3. (6, 6)

4. (-6, -6)

Q.

A point P (3, 5) is reflected in line y + 4 = 0 to form the image P'. Find the coordinates of P'.

1. (3, -12)

2. (3, -13)

3. (3, -11)

4. (3, -10)

Q.

The reflection of the point (9, 6) on the line Y= 5 is

1. (4, 9)

2. (9, 4)

3. (2, 6)

4. (3, 6)

Q.

The reflection of the point (3, 5) in the line Y = 3 is ___

1. (3, 1)

2. (-3, 1)

3. (1, 3)

4. (1, -3)

Q.

What is the reflection of the point $A(-2,3)$ in the line $y=2$?

1. (-2, -1)

2. (-2, 1)

3. (3, 1)

4. (-2, -3)