Question

HELP ME ASAP!! 90 POINTS!!

Given the graph of rectangle QUAD and its reflection.

Use the coordinates of the images' vertices, Q and Q' to algebraically find the line of reflection. In your final answer, include all of your work.

Answer 1

x = 1/2

Explanation:

To find the line of reflection, we take the points and find the midpoint

u + u'

------ = line of reflection

2

We know the line of reflection is x=something since the y coordinates are the same

(-2) + (3) (1)

------------------ = ----------- = (1/2 )

2 2

x = 1/2

Lets check another point to verify

D = (-4, 1) (5,1)

(-4+5)/2 = 1/2

Answer 2

The line of reflection is
`x=0.5`.

Explanation:

Reflection is a rigid transformation. In reflection, the distance between preimage and line of reflection is equal to the distance between image and line of reflection.

Since the image and preimage are equidistant from the line of reflection, therefore the line of reflection is passing through the midpoints of image and preimage.

From the given figure it is noticed that the vertices of U(-2,2), D(-4,-1), U'(3,2) and D'(5,-1).

Midpoint of UU'.

`((-2+3)/(2),(2+2)/(2))=(0.5,2)`

Midpoint of UU'.

`((-4+5)/(2),(-1-1)/(2))=(0.5,-1)`

The line of reflection passing through the points (0.5,2) and (0.5,-1).

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-2=(-1-2)/(0.5-0.5)(x-0.5)`

`x=0.5`

Therefore line of reflection is
`x=0.5`.