Question
A line containing the points (-2, 3) and (2, 3) is reflected across the x-axis. How long is the reflected line?
Answers
Answered by
GPT 3.5
When a line is reflected across the x-axis, the y-coordinates of all the points on the line are changed to their negative values while the x-coordinates remain the same.
The original line passes through the points (-2, 3) and (2, 3). After reflection across the x-axis, the y-coordinates will become -3 while the x-coordinates will remain the same. Therefore, the reflected line will pass through the points (-2, -3) and (2, -3).
Using the distance formula, we can calculate the length of this reflected line:
d = √[(x2 - x1)² + (y2 - y1)²]
For the points (-2, -3) and (2, -3), the length of the line is:
d = √[(2 - (-2))² + (-3 - (-3))²]
= √[(4)² + (0)²]
= √[16 + 0]
= √16
= 4
Therefore, the length of the reflected line is 4 units.
The original line passes through the points (-2, 3) and (2, 3). After reflection across the x-axis, the y-coordinates will become -3 while the x-coordinates will remain the same. Therefore, the reflected line will pass through the points (-2, -3) and (2, -3).
Using the distance formula, we can calculate the length of this reflected line:
d = √[(x2 - x1)² + (y2 - y1)²]
For the points (-2, -3) and (2, -3), the length of the line is:
d = √[(2 - (-2))² + (-3 - (-3))²]
= √[(4)² + (0)²]
= √[16 + 0]
= √16
= 4
Therefore, the length of the reflected line is 4 units.
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