octogonalcreature877
contestada

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'?

Respuesta :

MathGeek289
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)
Ver imagen MathGeek289

The ordered pair of [tex]X'[/tex] is  [tex](3,3)[/tex]

Explanation

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

The triangle [tex]XYZ[/tex] is reflected across the line  [tex]y=1[/tex]  to create triangle [tex]X'Y'Z'[/tex]

Distance of the point [tex]X[/tex] from the line  [tex]y=1[/tex]  is  2 units.

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

[tex]y[/tex] co-ordinate of the point [tex]X'[/tex] will be:  [tex]y=1+2 =3[/tex]

So, the ordered pair of [tex]X'[/tex] is  [tex](3,3)[/tex]

Ver imagen Sicista

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