Question

Help me please.

Find the coordinates of J' after a reflection across the line x=1 and then across the x axis.

Answer 1

when j is reflected across the line of x=1 the j will become j'= 3 , then reflected again across the x - axis the j will become j''= -3. So your answer is -3

Answer 2

J'' = (0, 1)

Explanation:

For M being the midpoint of the segment JJ', its coordinates are the average of those of J and J':

M = (J + J')/2

We can rearrange this to find J' from M and J.

2M = J + J'

J' = 2M - J

For a reflection across the line x = 1, the x-coordinate of M is 1. For a reflection across the line y = 0 (the x-axis), the y-coordinate of M is 0. Your double reflection amounts to a reflection across the point (1, 0).

The the image of J after the two reflections is ...

J' = 2(1, 0) -(2, -1) = (2·1-2, 2·0+1)

J' = (0, 1)

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In the attached image, the point after the second reflection is called J".