Question

Triangle XYZ is shown on the coordinate plane below:

Triangle XYZ on the coordinate plane with ordered pairs at X 3, negative 1, at Y 4, negative 4, at Z 1, negative 2

If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'?

Answer 1

First, graph the triangle XYZ. Its points are:
(3, -1)
(4, -4)
(1, -2)
The triangle created is the first file attached.
When reflected off of the line y = 1, it is one higher y than reflecting off the y axis. So, the coordinates are (1,-4) (3, 3) (4, 6)

Answer 2

The ordered pair of
`X'` is
`(3,3)`

Step-by-step explanation

According to the below diagram, the co ordinates of
`\triangle XYZ` are:
`X(3, -1), Y(4,-4)` and
`Z(1,-2)`

The triangle
`XYZ` is reflected across the line
`y=1` to create triangle
`X'Y'Z'`

Distance of the point
`X` from the line
`y=1` is 2 units.

So, the point
`X'` will be also 2 units above the line
`y=1`. As the triangle is reflected across a horizontal line, so the
`x` co-ordinate of the point will remain same.

`y` co-ordinate of the point
`X'` will be:
`y=1+2 =3`

So, the ordered pair of
`X'` is
`(3,3)`