GREhelp wrote:
|a| > |c|
In the coordinate plane, points (a,b) and (c,d) are equidistant from the origin.
Quantity A |
Quantity B |
|B| |
|D| |
Here's another approach:
KEY PROPERTIES:
If x² > y² then |x| > |y|
If |x| > |y| then x² > y² GIVEN: (a,b) and (c,d) are equidistant from the origin. The origin has coordinates (0, 0)
When we apply the formula for finding the distance between two points, we get:
The distance between (a, b) and (0, 0) = √[(a - 0)² + (b - 0)²]
= √(a² + b²)
The distance between (c, d) and (0, 0) = √[(c - 0)² + (d - 0)²]
= √(c² + d²)
So, we can write: √(a² + b²) = √(c² + d²)
Square both sides to get: a² + b² = c² + d²
Subtract c² from both sides to get: a² + b² - c² = d²
Subtract b² from both sides to get:
a² - c² = d² - b²GIVEN: |a| > |c|This also tells us that a² > c²
If we subtract c² from both sides we get:
a² - c² > 0Since, we know that
a² - c² = d² - b², we can also conclude that
d² - b² > 0Now take
d² - b² > 0 and add b² to both sides to get: d² > b²
Finally, if d² > b², then we know that |d| > |b|
Answer: B
Cheers,
Brent
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Brent Hanneson - founder of Greenlight Test PrepSign up for our GRE Question of the Day emails