Reflect triangle ABC with respect to the x -axis and the y -axis. What are the vertices of triangle A′B′C′
1.The vertices of triangle A′B′C′ are A′(−2,1), B′(−1,3), and C′(−6,3)
2.The vertices of triangle A′B′C′ are A′(2,1), B′(6,3), and C′(1,3).
3.The vertices of triangle A′B′C′ are A′(−2,1), B′(−6,3), and C′(−1,3)
4.The vertices of triangle A′B′C′ are A′(−2,−1), B′(−6,−3), and C′(−1,−3).
The correct answer is 3. The vertices of triangle A′B′C′ are A′(−2,1), B′(−6,3), and C′(−1,3).
When reflecting a point with respect to the x-axis, the y-coordinate stays the same and the sign of the x-coordinate changes. Similarly, when reflecting a point with respect to the y-axis, the x-coordinate stays the same and the sign of the y-coordinate changes.
Therefore, to reflect triangle ABC with respect to the x-axis, we change the sign of the y-coordinates of each vertex. To reflect triangle ABC with respect to the y-axis, we change the sign of the x-coordinates of each vertex.
Starting with triangle ABC with vertices A(2,1), B(6,3), and C(1,3), reflecting it with respect to the x-axis gives us triangle A′B′C′ with vertices A′(2,-1), B′(6,-3), and C′(1,-3). Then reflecting it with respect to the y-axis gives us A′(−2,-1), B′(−6,-3), and C′(−1,-3).
Therefore, the correct answer is 3. The vertices of triangle A′B′C′ are A′(−2,1), B′(−6,3), and C′(−1,3).