Question

Given that the triangle ABC is at A = ( 5, 5 ) B = ( 2, 8 ) C = ( 9, 7 ), and if the triangle is reflected across the line y = 3, find the new position of point C'.

Answer 1

A. (9, -1)

Explanation:

Given the triangle ABC, the coordinate of point C is:

`C=(9,7)`

We want to reflect C across the line y=3.

Comparing the y-coordinate of C and the given line:

`\begin{gathered} 3+x=7 \\ 3+4=7 \\ \implies x=4 \end{gathered}`

Since the point and its image must be the same distance from the line of reflection, the y-value of the image point, C' will be:

`3-4=-1`

Thus, the new position of C' will be:

`C^(\prime)=(9,-1)`

Option A is correct.