Question

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)

2. 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':

Answer 1

A, B, A

Explanation:

Answer 2

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.

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.