Question

The coordinates of the vertices of ΔPQR are (–2, –2), (–6, –2), and (–6, –5).

The coordinates of the vertices of ΔPʹQʹRʹ are (−2, 2), (−6, 2), and (−6, 5).
This transformation can be expressed as (x, y) → (x, −y).

PLEASE HELP ME!!

Is ΔPQR congruent to ΔPʹQʹRʹ? Why or why not?

answers:

No, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis.

Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis.

Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the y-axis.

No, ΔPʹQʹRʹ is a reflection of ΔPQR over the y-axis.

Answer 1

Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis

Step-by-step explanation:

The problem statement tells you the transformation is ...

... (x, y) → (x, -y)

Consider the two points (0, 1) and (0, -1). These points are chosen for your consideration because their y-coordinates have opposite signs—just like the points of the transformation above. They are equidistant from the x-axis, one above, and one below. Each is a reflection of the other across the x-axis.

Along with translation and rotation, reflection is a transformation that does not change any distance or angle measures. (That is why these transformations are all called "rigid" transformations: the size and shape of the transformed object do not change.)

An object that has the same length and angle measures before and after transformation is congruent to its transformed self.

So, ... ∆P'Q'R' is a reflection of ∆PQR over the x-axis, and is congruent to ∆PQR.