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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.
Write down the co-ordinates of A and B and draw a diagram to represent this information.

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To find the coordinates of points A and B based on the given information about their reflections in the origin, we follow these steps: ### Step 1: Understand the Reflection in the Origin The reflection of a point (x, y) in the origin is given by the coordinates (-x, -y). This means that if we know the coordinates of the reflected points A1 and B1, we can find the original points A and B by changing the signs of their coordinates. ### Step 2: Identify the Coordinates of A1 and B1 We are given: - A1 = (4, -5) - B1 = (-7, 0) ### Step 3: Calculate the Coordinates of A Using the reflection formula: - A = (-x, -y) for A1 = (4, -5) So, \[ A = (-4, 5) \] ### Step 4: Calculate the Coordinates of B Using the reflection formula: - B = (-x, -y) for B1 = (-7, 0) So, \[ B = (7, 0) \] ### Step 5: Summarize the Coordinates The coordinates of points A and B are: - A = (-4, 5) - B = (7, 0) ### Step 6: Draw the Diagram To represent this information visually: 1. Draw a Cartesian coordinate system with x and y axes. 2. Plot the origin O at (0, 0). 3. Plot point A at (-4, 5). 4. Plot point B at (7, 0). 5. Plot points A1 at (4, -5) and B1 at (-7, 0) to show the reflection. 6. Connect the points O, A, and B to form triangle OAB, and O, A1, and B1 to form triangle OA1B1. ### Final Coordinates: - A = (-4, 5) - B = (7, 0) ---
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