Special Case When Y = a = 0

Q.

The area of the triangle formed by the line x/a+y/b=1 with the coordinate axes is

Q.

The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A".

(i) Write down the co-ordinates of A".

(ii) Write down a single transformation that maps A onto A".

Q.

Which rule describes the transformation that is reflection across the $x$ axis?

Q.

The reflection of a point (x, y) in the x axis is

1. (x, -y)

2. (-x, y)

3. (-x, -y)

4. (x, y)

Q.

The vertices of a figure are given. Find the coordinates of the image after the transformations given.

$\mathrm{A}(-5,3),\mathrm{B}(-2,3),\mathrm{C}(-2,1),\mathrm{D}(-5,1)$

Reflect in the $\mathrm{y}-$axis. Then, dilate using a scale factor of $2$.

Q.

State the co-ordinates of the following points under reflection in the line y - 0;

(i) (-3, 0) (ii) (8, -5) (iii) (-1, -3)

Q.

A, B and C are the points on a coordinate plane. The $\Delta ABC$ is a right-angled triangle (right-angled at C ). If $AC$ is parallel to the X-axis and the angle between $AB$ and $AC$ is ${45}^o$. The slope of $AB$ is___ .

1. 1

2. 0

3. $\sqrt{2}$

4. not defined

Q.

Use graph paper for the question.

The point P(2, -4) is reflected about the line = 0 to get the image Q. Point Q is reflected by the line y = 0 to get the image R.

Find area of figure PQR.

1. 8 units²

2. 10 units²

3. 12 units²

4. 14 units²

5. 16 units²

Q. The coordinates of a point P are (2, 5). Given that the image of P under a reflection in the-x-axis is P, find the coordinates of P.

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

Q. The image of the point $(4,-3)$ under a reflection across the x-axis is:

1. $(-4,3)$
2. $(-4,-3)$
3. $(4,3)$
4. None of these

Q.

Point Transformation Image

(6, 10) ____ (6, -10)

1. y = 0

2. X-axis

3. Y-axis

4. x = 0

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. 9
3. 6
4. 12

Q. State the co-ordinates of the following points under reflection in the line $x=0:$
$(3,-4)$

Q. A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching the $x$-axis, an equation of the reflected ray is

1. $y=x+\sqrt{3}$
2. $\sqrt{3y}=x+\sqrt{3}$
3. $y=\sqrt{3x}-\sqrt{3}$
4. $\sqrt{3y}=x-1$

Q.

The image of a point P(x, y) when reflected in the X-axis is ___.

1. (0, -y)

2. (x, -y)

3. (-x, y)

4. (-x, 0)

Q. A ray of light passing through in point (1, 2) reflate on the x-axis at point A and line reflected ray passed through the point (5, 3) co-ordinates of A= ___

1. $(\frac{13}{5},0)$
2. $(-\frac{13}{5},0)$
3. $(0,\frac{13}{5})$
4. none of these

Q. A circle with centre $(0,0)$ and of radius $2$ cm is plotted in the XY plane. Take the part of circle in first quadrant and find its reflection through X axis.

1. The reflected image will form in $1st$ quadrant.
2. The reflected image will form in $2nd$ quadrant.
3. The reflected image will form in $4rth$ quadrant.
4. The reflected image will form in $3rd$ quadrant.

Q.

The image of a point P reflected in the x- axis is $(-3,2)$. The co-ordinates of P will be ?.

1. $P(3,-2)$

2. $P(-3,2)$

3. $P(-3,-2)$

4. $P(3,2)$

Q. State the co-ordinates of the following points under reflection in x-axis:
$(3,2)$

Q.

Reflection of the point $(-10,7)$ in the x-axis is ____________

1. (10, 7)

2. (-10, 7)

3. (-10, -7)

4. (0, -7)

Q. A ray of light passing through the point $(1,2)$ is reflected on the $x$-axis at a point $P$ and passes through the point $(5,3)$. The abscissa of the point $P$ is

1. $3$
2. $\frac{13}{3}$
3. $\frac{13}{5}$
4. $\frac{13}{4}$

Q. When a point is reflected in x-axis the sign of its ordinate changes.

1. False
2. True

Q.

A point P (x, y) is reflected in the X axis and its image is (-4, 5), the value of x and y is ____

1. (-4, -5)

2. (4, -5)

3. (-4, 5)

4. (4, 5)

Q. 26. Use graph paper to answer this question
(i) Plot the points A (4, 6) and B (1, 2).
(ii) If A’ is the image of A when reflected in x-axis, write the co-ordinates of A’.
(iii) If B’ is the image of B when B is reflected in the line AA’, write the co-ordinates of B’.
(iv) Give the geometrical name for the figure ABA’B’.

Q. A point P (a, b) is reflected in the x-axis to P’ (2, -3), write down the values of a and b. P” is the image of P, when reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”, when P is reflected in the line parallel to y-axis such that x = 4.

Q. State the co-ordinates of the following points under reflection in x-axis:
$(0,0)$

Q. The triangle ABC where A (1, 2), B (4, 8), C (6, 8) is reflected in the x-axis to triangle A’ B’ C’. The triangle A’ B’ C’ is then reflected in.the origin to triangle A”B”C” Write down the co-ordinates of A”, B”, C”. Write down a single transformation that maps ABC onto A” B” C”.

Q. Find the co ordinate of the point which we get by reflecting (-2, 3) through x-axis.

Q. State the co-ordinates of the following points under reflection in the line $x=0:$
$(0,5)$

Q.

Identify the shaded region in the figure. A and B are two sets represented by the circles. U is the universal set, which is represented by the rectangle.

1. A - B

2. B- (AUB)

3. A-(AUB)

4. U-B'-( A∩B)