Question

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

Answer 1

Answer:

True

Step-by-step 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.

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

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

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

$D= \sqrt{(x - x)^2 + (0 - y)^2}$

$D= \sqrt{(0)^2 + (- y)^2}$

$D= \sqrt{0 + y^2}$

$D= \sqrt{y^2}$

$D = y$

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

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

$D= \sqrt{(x - x)^2 + (0 - (-y))^2}$

$D= \sqrt{(0)^2 + (0+y)^2}$

$D= \sqrt{0 + y^2}$

$D= \sqrt{y^2}$

$D = y$

See that the calculated distance are equal.

Hence, the given statement is true