Question

Find the coordinates of each point after the described reflection. Give the distance between each point and its reflection.

Answer 1

Complete Question:

Find the coordinates of the point after the described reflection. Give the distance between the point and its reflection. R(-5, 8) is reflected across the x-axis _____________.

Answer:

`(a)`
`R' = (-5,-8)`

`(b)` The distance is 16 units

Explanation:

Given

`R = (-5,8)`

Solving (a): Reflection across x-axis

The rule is:

`R(x,y) ==> R(x,-y)`

So, the reflection of
`R = (-5,8)` is:

`R' = (-5,-8)`

Solving (b): The distance between R and R'

Distance (d) is calculated as:

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)`

Where:

`R = (-5,8)` ----
`(x_1,y_1)`

`R' = (-5,-8)` ---
`(x_2,y_2)`

This gives:

`d = √((-5- -5)^2 + (-8- 8)^2)`

`d = √((0)^2 + (-16)^2)`

`d = √(256)`

`d = 16`

The distance is 16 units