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

Step-by-step 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:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Where:

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

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

This gives:

$d = \sqrt{(-5- -5)^2 + (-8- 8)^2}$

$d = \sqrt{(0)^2 + (-16)^2}$

$d = \sqrt{256}$

$d = 16$

The distance is 16 units