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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'.

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 class=

Respuesta :

Answer:

A. (9, -1)

Explanation:

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

[tex]C=(9,7)[/tex]

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

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

[tex]\begin{gathered} 3+x=7 \\ 3+4=7 \\ \implies x=4 \end{gathered}[/tex]

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:

[tex]3-4=-1[/tex]

Thus, the new position of C' will be:

[tex]C^{\prime}=(9,-1)[/tex]

Option A is correct.

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