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:
[tex](a)[/tex] [tex]R' = (-5,-8)[/tex]
[tex](b)[/tex] The distance is 16 units
Step-by-step explanation:
Given
[tex]R = (-5,8)[/tex]
Solving (a): Reflection across x-axis
The rule is:
[tex]R(x,y) ==> R(x,-y)[/tex]
So, the reflection of [tex]R = (-5,8)[/tex] is:
[tex]R' = (-5,-8)[/tex]
Solving (b): The distance between R and R'
Distance (d) is calculated as:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Where:
[tex]R = (-5,8)[/tex] ---- [tex](x_1,y_1)[/tex]
[tex]R' = (-5,-8)[/tex] --- [tex](x_2,y_2)[/tex]
This gives:
[tex]d = \sqrt{(-5- -5)^2 + (-8- 8)^2}[/tex]
[tex]d = \sqrt{(0)^2 + (-16)^2}[/tex]
[tex]d = \sqrt{256}[/tex]
[tex]d = 16[/tex]
The distance is 16 units
