Question

When a point is reflected across a line of reflection, it remains the same distance from the line.True or False

Answer 1

True

Explanation:

To answer this question, I will use the following illustrations.

Assume a point (x,y) is reflected across the x-axis.

Using reflection rule, the new point will be: (x,-y)

On a coordinate plane, the x-axis is represented as: (x,0)

So, we will calculate the distance between (x,y) and (x,0) and also calculate the distance between (x,-y) and (x,0) using the following distance formula.

`D= √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Distance between (x,y) and (x,0)

`D= √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`D= √((x - x)^2 + (0 - y)^2)`

`D= √((0)^2 + (- y)^2)`

`D= √(0 + y^2)`

`D= √(y^2)`

`D = y`

Distance between (x,-y) and (x,0)

`D= √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`D= √((x - x)^2 + (0 - (-y))^2)`

`D= √((0)^2 + (0+y)^2)`

`D= √(0 + y^2)`

`D= √(y^2)`

`D = y`

See that the calculated distance are equal.

Hence, the given statement is true