Which graph shows a triangle and its reflection image across the y-axis? (1 point) Responses The first triangle has vertices at left-parenthesis negative 4 comma 3 right-parenthesis, left-parenthesis negative 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis 4 comma 3 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 4 comma 3 right-parenthesis, left-parenthesis negative 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis 4 comma 3 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The first triangle has vertices at left-parenthesis negative 5 comma 2 right-parenthesis, left-parenthesis negative 1 comma 2 right-parenthesis, and left-parenthesis negative 1 comma 4 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis. Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 5 comma 2 right-parenthesis, left-parenthesis negative 1 comma 2 right-parenthesis, and left-parenthesis negative 1 comma 4 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis. The first triangle has vertices at left-parenthesis negative 3 comma 3 right-parenthesis, left-parenthesis negative 1 comma 3 right-parenthesis, and left-parenthesis negative 1 comma negative 1 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis. Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 3 comma 3 right-parenthesis, left-parenthesis negative 1 comma 3 right-parenthesis, and left-parenthesis negative 1 comma negative 1 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis. The first triangle has vertices at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 3 comma 3 right-parenthesis, and left-parenthesis 3 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis negative 1 comma negative 1 right-parenthesis, left-parenthesis 3 comma negative 3 right-parenthesis, and left-parenthesis 3 comma negative 1 right-parenthesis. Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 3 comma 3 right-parenthesis, and left-parenthesis 3 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis negative 1 comma negative 1 right-parenthesis, left-parenthesis 3 comma negative 3 right-parenthesis, and left-parenthesis 3 comma negative 1 right-parenthesis. Skip to navigation
The correct response is: The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1). Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1).
The correct answer is the first triangle with vertices at (-4,3), (-4,1), and (0,1), where the reflection image across the y-axis is the second triangle with vertices at (4,3), (4,1), and (0,1).
To determine which graph shows a triangle and its reflection image across the y-axis, we need to understand what happens when a shape is reflected across the y-axis.
When a shape is reflected across the y-axis, the x-coordinates of its points are negated while the y-coordinates remain unchanged. This means that each point will have its x-coordinate flipped to its opposite sign while the y-coordinate remains the same.
Let's examine the given options:
1. The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1).
2. The first triangle has vertices at (-5, 2), (-1, 2), and (-1, 4). The second triangle has vertices at (0, 1), (4, 3), and (4, 1).
3. The first triangle has vertices at (-3, 3), (-1, 3), and (-1, -1). The second triangle has vertices at (0, 1), (4, 3), and (4, 1).
4. The first triangle has vertices at (-1, 1), (3, 3), and (3, 1). The second triangle has vertices at (-1, -1), (3, -3), and (3, -1).
To reflect a triangle across the y-axis, we negate the x-coordinates of each vertex. Comparing the given options with this transformation, we find that only option 1 satisfies the condition. The first triangle in option 1 has vertices at (-4, 3), (-4, 1), and (0, 1), and when reflected across the y-axis, the triangle will have vertices at (4, 3), (4, 1), and (0, 1), which matches the second triangle in option 1.
Therefore, the graph that shows a triangle and its reflection image across the y-axis is the one in option 1.