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Triangle OA(1)B(1) is the reflection of ...

Triangle `OA_(1)B_(1)` is the reflection of triangle OAB in origin, where `A_(1) (4, -5)` is the image of A and `B_(1) (-7, 0)` is the image of B.
Find the co-ordinates of `A_(2)`, the image of A under reflection in x-axis followed by reflection in y-axis.

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The correct Answer is:
To find the coordinates of \( A_2 \), the image of point \( A \) under reflection in the x-axis followed by reflection in the y-axis, we can follow these steps: ### Step 1: Find the coordinates of point A Given that \( A_1(4, -5) \) is the reflection of point \( A \) in the origin, we can find the coordinates of \( A \) by negating the coordinates of \( A_1 \). \[ A = (-x, -y) = (-4, 5) \] ### Step 2: Reflect point A in the x-axis To reflect a point \( (x, y) \) in the x-axis, we change the sign of the y-coordinate. Therefore, the reflection of point \( A(-4, 5) \) in the x-axis is: \[ A' = (-4, -5) \] ### Step 3: Reflect point A' in the y-axis To reflect a point \( (x, y) \) in the y-axis, we change the sign of the x-coordinate. Thus, the reflection of point \( A'(-4, -5) \) in the y-axis is: \[ A_2 = (4, -5) \] ### Final Answer The coordinates of \( A_2 \) are \( (4, -5) \). ---
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