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Point Slope Form of a Line

The point 4,1...

Question

The point (4,1) undergoes the following three transformations successively:-

i) Reflection about the line y=x

ii)Translation through a distance of 2units along the positive direction of X axis.The final position of the point is

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Q. The point (4,1) undergoes the following three transformations successively-
(i) Reflection about the line

y = x

(ii) Translation through a distance 2 units along the positive directions of x-axis.
(iii) Rotation through an angle

\frac{π}{4}

about the origin.
The final position of the point is given by the coordinates:

(4, 1)

undergoes the following three transformations successively:
(I) Reflection about the line

y = x

(II) Translation through a distance

2

units along the positive direction of

x

-axis.
(III) Rotation of coordinate axes through an angle

\frac{π}{4}

about the origin in the clockwise direction.
The final position of the point is given by the coordinates

A (4, 1)

undergoes following transformations successively :
(i) reflection about line

y = x

(ii) translation through a distance of

3

units in the positive direction of

x

-axis
(iii) rotation through an angle

105^{\circ}

in anti-clockwise direction about origin

O

.
Then the final position of point

A

Q. If the point

P (4, 2)

undergoes the following transformations successively.

i)

Reflection about the line

y = x,

i i)

Translation through a distance of

5

units along the positive

x -

i i i)

Reflection about

y = 0

.
Then the coordinates of final position of

P

The point $(4, 1)$ undergoes the following transformations successively:

$(i)$ Reflection about the line $y = x - 1$

$(i i)$ Translation by one unit along x-axis in the positive direction.

$(i i i)$ Rotation through an angle $\frac{π}{4}$ about the origin in the anticlockwise direction.

The coordinates of $P$ in the final position are

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