Line q is defined by the equation y = mx + b, where m < 0. Does line q pass through (5,4)?
(1) When it is reflected around the x-axis, line q passes through (3,-4)
(2) When it is reflected around the y-axis, line q passes through (-5,3)
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1. Since the line reflected around the x axis contains point (3,-4), so the actual line should pass through (3,4). [Mirror reflection of the point around X-axis.]
Now, for the line to pass though (5,4), it should have a zero slope since it is already passing through (3,4). But our question states that slope of the line, m <0. So the line obtained from option 1 can't pass through (5,4). This option is sufficient.
2. Since the line reflected around the y axis contains point (-5,3), so the actual line should pass through (5,3). [Mirror reflection of the point around Y-axis.]
Now, for the line to pass though (5,3), it should have an infinite slope since it is already passing through (5,3). But our question states that slope of the line, m <0. So the line obtained from option 1 can't pass through (5,4). This option is sufficient.
Answer= Either of the options is sufficient. Hence D
Now, for the line to pass though (5,4), it should have a zero slope since it is already passing through (3,4). But our question states that slope of the line, m <0. So the line obtained from option 1 can't pass through (5,4). This option is sufficient.
2. Since the line reflected around the y axis contains point (-5,3), so the actual line should pass through (5,3). [Mirror reflection of the point around Y-axis.]
Now, for the line to pass though (5,3), it should have an infinite slope since it is already passing through (5,3). But our question states that slope of the line, m <0. So the line obtained from option 1 can't pass through (5,4). This option is sufficient.
Answer= Either of the options is sufficient. Hence D
