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  1. In the graph, the coordinates of the vertices of quadrilateral ABCD are A(-27,17), B(24,14), C(19,3) and D(-7,7) If quadrilateral EFGH is created as the image of quadrilateral ABCD reflected across the x-axis, find the coordinates of the vertex located at point E.

Graph:1

A(-27,-17)
B(-24,-14)
C(-19,-3)

D.(-7.-7)

  1. In the graph, triangle EFG is a reflection of preimage triangle ABC. AB=46 unitts, BC=44 units, and AC=10 units. Find the length of FG.

Graph 2


A: FG=10 units

B: FG= 44 units

C: FG= 46 units

D: FG= 56 units


3.Describe the change that occurs to the coordinates of a vertex of a figure when it is reflected across the y-axis.


A.The sign of the x-coordinate changes; the y-coordinate stays the same.

B.The x-coordinate stays the same; the sign of the y-coordinate changes.

C.Both coordinates stay the same.

D.The sign of each coordinate changes.


Please help? D':

In the graph, the coordinates of the vertices of quadrilateral ABCD are A(-27,17), B(24,14), C(19,3) and D(-7,7) If quadrilateral EFGH is created as the image o class=
In the graph, the coordinates of the vertices of quadrilateral ABCD are A(-27,17), B(24,14), C(19,3) and D(-7,7) If quadrilateral EFGH is created as the image o class=

Verified Answer :

Answer:

1. The coordinates of E are (-27,-17). The correct option is A.

2. The length of FG is 44 units. The correct option is B.

3. The correct option is A. The sign of the x-coordinate changes; the y-coordinate stays the same.

Step-by-step explanation:

1.

The vertices of quadrilateral ABCD are A(-27,17), B(24,14), C(19,3) and D(-7,7).

The quadrilateral EFGH is created as the image of quadrilateral ABCD reflected across the x-axis.

If a figure reflected across the x-axis, then

\((x,y)\rightarrow (x,-y)\)

\(A(-27,17)\rightarrow E(-27,-17)\)

Therefore the coordinates of E are (-27,-17). The correct option is A.

2.

Triangle EFG is a reflection of preimage triangle ABC. AB=46 unitts, BC=44 units, and AC=10 units.

Reflection is a rigid transformation. It means the image an preimage are congruent.

\(\triangle EFG\cong\triangle ABC\)

Corresponding parts of congruent triangles are congruent.

\(FG=BC\)             (CPCTC)

\(FG=44\)

Therefore the length of FG is 44 units. The correct option is B.

3.

If a figure reflected across the x-axis, then

\((x,y)\rightarrow (-x,y)\)

The sign of the x-coordinate changes; the y-coordinate stays the same.

Therefore the correct option is A.

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