If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′ lie?Group of answer choices(1, 1)(−4, 1)(−4, −1)(1, −1)
Question
If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′ lie?Group of answer choices(1, 1)(−4, 1)(−4, −1)(1, −1)
Solution
To answer this question, let's take each transformation step by step.
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Reflection over the y-axis: This transformation changes the sign of the x-coordinate. So if point A was at (x, y), after this transformation, A' would be at (-x, y).
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Reflection over the x-axis: This transformation changes the sign of the y-coordinate. So if after the first transformation, A' was at (-x, y), after this transformation, A' would be at (-x, -y).
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Rotation of 180°: This transformation changes the signs of both the x and y coordinates. So if after the second transformation, A' was at (-x, -y), after this transformation, A' would be at (x, y).
So, after all these transformations, point A' would be back at its original position. Therefore, without knowing the original coordinates of point A, we cannot definitively answer where point A' would lie.
Similar Questions
What set of reflections and rotations would carry rectangle ABCD onto itself?Group of answer choicesRotate 180°, reflect over the y-axis, reflect over the line y = xReflect over the x-axis, rotate 180°, reflect over the x-axisRotate 180°, reflect over the x-axis, reflect over the line y = xReflect over the y-axis, reflect over the x-axis, rotate 180°
Given ABC at A (-3, 2), B (-1, 3), C (-4, 5), and if the is first reflected over the y-axis, and then over the x-axis, find the coordinate ofA''.
Given ABC with points A = (5, 3), B = (-1, 3), C = (-4, 6), and if the is first reflected over the x-axis, and then over the y-axis, find the new location of A''.
If A has coordinates (2, -4) and is reflected over the y-axis, find the coordinates ofA'.
Question promptThe triangle ABC is reflected in the y-axis. What are the new coordinates of point C after the reflection?Question response areaSelect one option(0,4)(-2,-4)(2,4)(4,2)
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