Question

Find the coordinates of M' after a reflection across the line y= -1 and then across the line x= -2. Answer in form (a,b)

Answer 1

Answer:  (-1,3)

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Explanation:

Point M is currently located at (-3, -5). Note the y coordinate is y = -5. The vertical distance from this y coordinate to y = -1 is 4 units. If we move another 4 units up from y = -1, we end up at y = 3.

What does this mean? It means that reflecting point M over the line y = -1 has it end up on (-3, 3), which I'll call point N. See the diagram below.

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Next we reflect over the line x = -2. The horizontal distance from x = -3 to x = -2 is one unit. So we move another unit to the right to end up at x = -1.

Therefore, reflecting (-3,3) over the line x = -2 will have the point land on (-1, 3)

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When we reflect over the line y = -1 first and then the line x = -2 second, we will have the point (-3, -5) move to (-3,3) and then to (-1,3) in that order.

Check out the diagram below.