U4 L9 Question 1

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Question
Using triangle ABC with coordinates A(5,3) B(-2,7) C(-3,-8). Reflect the triangle across the line x =3 and then reflect across the line y=-2. What are the coordinates of A''?(1 point)
Responses

(1,-7)
(1,-7)

(5,6)
(5,6)

(1,3)
(1,3)

(-3,-8)

Answer 1

To find the coordinates of point A after the two reflections, we can follow these steps:

1. Reflect point A(5, 3) across the line x = 3:

   • The x-coordinate of A is 5, and reflecting across the line x = 3 means we find the distance from 5 to 3, which is \(5 - 3 = 2\). The reflected point will be the same distance on the opposite side of the line, so we subtract this distance from 3:
   • New x-coordinate: \(3 - 2 = 1\)
   • The y-coordinate remains the same: 3.
   • Thus, A' after the first reflection is A'(1, 3).

2. Now reflect point A'(1, 3) across the line y = -2:

   • The y-coordinate of A' is 3, and reflecting across the line y = -2 means we find the distance from 3 to -2, which is \(3 - (-2) = 5\). The reflected point will be the same distance on the opposite side of the line, so we subtract this distance from -2:
   • New y-coordinate: \(-2 - 5 = -7\)
   • The x-coordinate remains the same: 1.
   • Thus, A'' after the second reflection is A''(1, -7).

So the final coordinates of A'' are (1, -7).

The correct response is: (1, -7)