What is the rule for the reflection?

A reflection is an example of a transformation that takes a shape (called the pre-image) and flips it across a line (called the line of reflection) to create a new shape (called the image).

The most common lines of reflection are the x-axis, the y-axis, or the lines y=x or y=−x.

The x-axis,

Reflection across the x-axis: (3,2)→(3,−2)

i.e. for reflection across the x-axis the x-coordinate remains same and y-coordinate change to negative sign.

The y-axis

Reflection across the y-axis: (3,2)→(-3,2)

i.e. for reflection across the y-axis the y-coordinate remains same and x-coordinate change to negative sign.

The line y=x

Reflection across the line y=x: (3,2)→(2,3)

For reflection across y=x the x and y value get interchanged.

The line y=−x.

Reflection across the line y=−x: (3,2)→(−2,−3)

For reflection across y=-x the x and y value get interchanged with opposite signs.

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step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true