rahulvsd wrote: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)
[spoiler]OA: D Source: Grockit[/spoiler]
Few things must be noted about the reflection around axes:
1. If the mirror line is the x-axis, just change each (x, y) into (x, -y).
2. If the mirror line is the y-axis, just change each (x, y) into (-x, y).
The line q will pass through (5, 4) only if 4 = 5 m + b, hence the rephrased question is:
Is b = 4 = 5 m?
(1) When it is reflected around the x-axis, line q passes through (3, -4). This means that point (3, 4) is on line y = m x + b, hence 4 = 3 m + b or b = 4 - 3 m. In case m ≠0, b = 4 - 3 m proves that b ≠4 = 5 m. Sufficient
(2) When it is reflected around the y-axis, line q passes through (-5, 3). This means that point (5, 3) is on line y = m x + b, hence 3 = 5 m + b or b = 3 - 5 m. Since 3 is not 4, it proves that b ≠4 = 5 m. [spoiler]
Sufficient
Take D[/spoiler]
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The Princeton Review - Manya Abroad
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