Question

A. What is the equation of the line of reflection that reflects point P onto P' ?B. What is the equation of the line of reflection that reflects point P' onto P" ?C. Could P" also be a rotation of point P? If so, what is the center of rotation and how many degrees was point P rotated?

Answer 1

A) line x = 0

B) line y = 0

C) rotation of 180 degrees

Step-by-step explanation:

A) To get the line of reflection, we will use the coordinates of P and P'

P = (-3, 4)

P' = (3, 4)

From P to P', we see the x coordinate of P was negated while keeping y coordinate constant in order to get P'

`\begin{gathered} \text{Reflection over the y ax i}s\colon \\ (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ (-3,\text{ 4) }\rightarrow(-(-3),4)=(3,\text{ 4)} \\ \text{Hence, it is a reflectiom over the y a x i}s \\ \\ \text{Reflection of line x = 0} \end{gathered}`

B) From P' to P'':

P' = (3, 4)

P'' = (3, -4)

We see the y is negated while keeping x constant

`\begin{gathered} (x,\text{ y) }\rightarrow(x,\text{ -y)} \\ (3,\text{ 4) }\rightarrow\text{ (3, -(4)) = (3, -4)} \\ A\text{ reflection over the x ax is} \\ \\ \text{Reflection of line y = 0} \end{gathered}`

C) P = (-3, 4)

P'' = (3, -4)

We see from P to P'': the x and y coordinate of P was negated to get the coordinates of P''

`\begin{gathered} (x,\text{ y) }\rightarrow\text{ (-x, -y)} \\ (-3,\text{ 4) }\rightarrow\text{ (-(-3), -4) = (3, -4)} \\ (x,\text{ y) }\rightarrow\text{ (-x, -y) is a rotation of 180 degr}ees \end{gathered}`
`\begin{gathered} \text{Yes, P'' could be a rotation of point P} \\ \text{Center of rotation is at the origin} \\ P\text{ was rotated 180 degr}ees \end{gathered}`