Question

reflections on the coordinate plane
reflections
a reflection ____ a figure over a line of __ in order to create a ____ image.
each reflected point of the figure should be the same distance from the line of ______ on the opposite side.
1 reflect triangle wxy over the y - axis. then answer a - c.
a. record the vertices of the pre - image and the image in the table.
pre - image image

b. describe how the reflection affected the x and y - values of each vertex.
x - values:
y - values:
c. how could you represent a reflection over the y - axis algebraically?
2 reflect triangle def over the x - axis. then answer a - c.
a. record the vertices of the pre - image and the image in the table.
pre - image image

b. describe how the reflection affected the x and y - values of each vertex.
x - values:
y - values:
c. how could you represent a reflection over the x - axis algebraically?

Explanation:

Step1: Identify pre - image vertices of triangle WXY

From the graph, the vertices of triangle WXY (pre - image) are W(2,6), X(6,4), Y(2,2).

Step2: Apply rule for reflection over y - axis

The rule for reflecting a point (x,y) over the y - axis is (-x,y). So, for W(2,6), the image is W'(- 2,6); for X(6,4), the image is X'(-6,4); for Y(2,2), the image is Y'(-2,2).

PRE - IMAGE	IMAGE
X(6,4)	X'(-6,4)
Y(2,2)	Y'(-2,2)

Step3: Analyze effect on x and y values

For a reflection over the y - axis, the x - values change sign and the y - values remain the same.

• x - values: Change sign.
• y - values: Remain the same.

Step4: Write algebraic representation for y - axis reflection

The algebraic representation of a reflection over the y - axis is (x,y)→(-x,y).

Step5: Identify pre - image vertices of triangle DEF

From the graph, the vertices of triangle DEF (pre - image) are D(2,-2), E(6,-7), F(2,-7).

Step6: Apply rule for reflection over x - axis

The rule for reflecting a point (x,y) over the x - axis is (x,-y). So, for D(2,-2), the image is D'(2,2); for E(6,-7), the image is E'(6,7); for F(2,-7), the image is F'(2,7).

PRE - IMAGE	IMAGE
E(6,-7)	E'(6,7)
F(2,-7)	F'(2,7)

Step7: Analyze effect on x and y values

For a reflection over the x - axis, the x - values remain the same and the y - values change sign.

• x - values: Remain the same.
• y - values: Change sign.

Step8: Write algebraic representation for x - axis reflection

The algebraic representation of a reflection over the x - axis is (x,y)→(x,-y).

Answer:

1.

• a.

PRE - IMAGE	IMAGE
X(6,4)	X'(-6,4)
Y(2,2)	Y'(-2,2)

• b. x - values: Change sign; y - values: Remain the same.
• c. (x,y)→(-x,y)

2.

• a.

PRE - IMAGE	IMAGE
E(6,-7)	E'(6,7)
F(2,-7)	F'(2,7)

• b. x - values: Remain the same; y - values: Change sign.
• c. (x,y)→(x,-y)