Question

So basically I have to reflect triangle STU across line ST and I need to find a valid reason of why the image of U will coincide with J. I need guidance please

Answer 1

- The reflection of an object across a line implies that the distance between the object and the reflection line is the same as the distance between the image and the reflection line.

- This implies that if the distance between the point U and the reflection line ST is x, then, the distance between the reflection line and the image of U must be a distance of x as well.

- This is illustrated below:

- From the above, we can see that distance x is a perpendicular distance from point U to reflection line ST.

- However, we must not just assume that distance x lands at point J.

- We can however show that this is the case because of the SSS congruency. That is,

`\begin{gathered} SU\cong SJ\text{ \lparen Given in the question\rparen} \\ UT\cong TJ\text{ \lparen Given in the question\rparen} \\ ST\text{ is a common side for both triangles SUT and SJT} \end{gathered}`

- Since both triangles are congruent, we can proceed to conclude that from line ST to point J is also a distance of x.

- Therefore, the image of U will coincide with J given that ST is the reflection line