REFLECTION ACROSS THE VERTICAL LINE

REFLECTION ABOUT VERTICAL LINE

To reflect the image about x = h, we have to draw the vertical line through h.

Calculate the distance between every vertices on the given shape.

To get the reflected image, we have to go in the opposite direction with the distance.

What is preimage ?

Preimage In a transformation, the original figure is called the preimage.

What is image ?

Image In a transformation, the final figure is called the image.

Example :

Find the coordinates of the vertices of each figure after the given transformation.

Reflection across x = 3

Solution :

By observing the points from the triangle given above,

A(1, 1) B (4, 4) and C (3, 0)

Problem 1 :

Find the coordinates of the vertices of each figure after the given transformation.

Reflection across x = 3

F (2, 2), W (2, 5), K (3, 2)

Solution :

Comparing the x-coordinates.

How to get F' ?

To get 2 (x-coordinate of F), we have to move 1 unit left. So, to get F', move 1 unit right.

F (2, 2) ==> F' (4, 2)

How to get W' ?

To get 2 (x-coordinate of W), we have to move 1 unit left. So, to get W', move 1 unit right.

W (2, 5) ==> W' (4, 5)

How to get K' ?

To get 3 (x-coordinate of K), So we don't have to move

K (3, 2)  ==> K' (3, 2)

Problem 2 :

Find the coordinates of the vertices of each figure after the given transformation.

 reflection across x = −1

V(−3, −1), Z(−3, 2), G(−1, 3), M(1, 1)

Solution :

Comparing the x-coordinates.

How to get V' ?

To get -3 (x-coordinate of V), we have to move 2 units left. So, to get V', move 2 units right from -1.

V (-3, -1) ==> V' (1, -1)

How to get Z' ?

To get -3 (x-coordinate of Z), we have to move 2 units left. So, to get Z', move 2 units right from -1.

 Z(−3, 2) ==>  Z'(1, 2)

How to get G' ?

To get -1 (x-coordinate of G), so we dont have to move.

G (−1, 3) ==> G' (−1, 3)

How to get M' ?

To get 1 (x-coordinate of Z), we have to move 2 units right. So, to get M', move 2 units left from -1.

M(1, 1) ==> M' (-3, 1)

Problem 3 :

Find the coordinates of the vertices of each figure after the given transformation.

Reflection across x = -3

Solution :

By observing the triangle given above,

P(-5, 2), Q(-2, 4) and R(-1, 2)

Find P' :

Reflection across x = -3

By comparing the -3 and x-coordinate of P, that is -5, to reach -5 from -3, we have to move 2 units left. To get P', move 2 units right.

P (-5, 2) ==> P' (-1, 2)

Find Q' :

By comparing the -3 and x-coordinate of P, that is -2, to reach -2 from -3, we have to move 1 units right. To get P', move 1 unit left.

Q (-2, 4) ==> Q' (-4, 4)

Find R' :

By comparing the -3 and x-coordinate of P, that is -1, to reach -1 from -3, we have to move 2 units right. To get P', move 2 units left.

R (-1, 2) ==> R' (-5, 2)