The rule (x, y)→(−x, y) maps △abc to △a′b′c′.
which statement correctly describes the relationship between △abc and △a′b′c′ ?
the triangles are congruent because △a′b′c′ is a rotation of △abc, and a rotation is a rigid motion.
the triangles are congruent because △a′b′c′
is a reflection of △abc, and a reflection is a rigid motion.
the triangles are not congruent because △a′b′c′
is a translation of △abc, and a translation is not a rigid motion.
the triangles are not congruent because △a′b′c′
is a reflection of △abc, and a reflection is not a rigid motion.

The correct option is :

(B)The triangle are congruent because the triangle A'B'C' is a reflection of triangle ABC and a reflection is a rigid motion.

Step-by-step explanation:

Given information:

The rule (x,y) going to (-x,y) maps triangle ABC to Triangle A'B'C'

Now,

The reflection is going on if we are going from (x,y) to (-x,y)

For example the point (1,3) will map (-1,3) , this is a reflection over y axis.

A reflection will keep the two points the same distance apart so we can say it will preserve the side length and distance.

Hence, if triangle ABC is reflected over y axis then A'B'C' is congruent to ABC.

So, The correct option is :

(B)The triangle are congruent because the triangle A'B'C' is a reflection of triangle ABC and a reflection is a rigid motion.

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if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this