Question

Decide whether the statement is true or false. If it is false, give the correct coordinates of N".If N(-2. 4) is reflected in the line y = 1. then N' is (-2-4).(Image down below)

Answer 1

Solution:

Given:

$N(-2,4)$

If the point is reflected in the line y = 1, this shows reflection over the x-axis but with a translation of 1 above the x-axis.

To reflect over the x-axis, the rule below applies;

$(x,y)\longrightarrow(x,-y)$

Hence,

$N(-2,4)\longrightarrow N^{\prime}(-2,-4)$

However, over the line y = 1, the y-coordinate of the reflected point N' will move up by 2units.

$\begin{gathered} N^{\prime}(-2,-4)\text{ will be;} \\ N^{\prime}(-2,-2) \end{gathered}$

Therefore, the statement given is FALSE.

The correct coordinates of N' is;

$N^{\prime}(-2,-2)$

The graph is as shown in the image below showing the reflection of N over y = 1 to give N'