coordinate geometry

Taniuca wrote:Which of the following lines is perpendicular to y=-2x+3 and has the same y-intercept as y=2x-3?

a) y=-1/2x+3
b) y= 1/2x-3
c) y= 1/2x+3
d) y= 2x+3
e) y = 2x-3

IMO B

to be perpendicular, the slope of the other line must be the opposite and negative, thus if the given slope is -2, the opposite and negative is 1/2.
the y intercept of the line is -3, thus the only option containing both is B

OA?

According to the Kaplan the right aswer is B y=1/2x-3

Good question - like most involving coordinate geometry, too, you don't need to know too specific a rule on this one...you can get by using logic.

To find the y-intercept (where the line crosses the y axis), you need to test the equation for where x = 0 (with x at zero, that's the y-axis). So you'd set x equal to 0, which just negates the entire x term in any of the answer choices. Only B and E have the same y-intercept, y = -3, as the original, so A, C, and D are all incorrect.

Then you can test for a line that's perpendicular to the original. If you look, though, E has the same slope (2) as the original, so it won't intersect it - they'll keep running parallel to each other. Therefore, E is incorrect, and B is the last man standing. Since you've proven the others to be incorrect, you don't even need to plot B as a line or rely on the lesser-used rule for perpendicular lines. B must be correct.

Often times, coordinate geometry questions can look as though they're from another world and take you back to graphing calculators and 7am high school classes. Usually, however, you can get by without having to have memorized specific coordinate formulas and rules:

-The coordinate plane is full of right angles, so use your knowledge of right triangles to find lengths and areas
-Lines will intersect each other at the same point, so to find an intersection you can just use algebra to find where x=x and y=y
-Etc.

A good working knowledge of coordinate geometry can certainly be helpful, but really only the basics are required...trust yourself that you can break a lot of coordinate geometry problems down to basic geometry and algebra. In most cases, the coordinate plane and its right-angles-galore will work distinctly to your advantage even if the idea of "coordinate geometry" on the surface seems intimidating.

Taniuca,

You only need a few concepts to do well on co-ordinate geometry questions, as Brian pointed out. One of the major things you should know is the slope-intercept form: y = mx + b. It is tested commonly enough on the GMAT to memorize.

The x and y are the coordinate, the m is the slope, and the b is the y-intercept. Using this information, this problem is rather straight forward. You know you want the same y-intercept as y=2x - 3, so eliminate A, C, and D.

One of the other few useful things to know about coordinate geometry is the relationship between slopes. Parallel slopes are equal to each other, and perpendicular slopes are negative reciprocals of each other. Since we want a perpendicular slope for the equation y= -2 + 3, we look for 1/2 as our desired perpendicular slope.

As pointed earlier in the thread, you don't need most equations for coordinate geometry. However, in my experience, I have seen perpendicular lines tested enough to bother learning the simple rule: negative reciprocal for the slope.

I hope that helps!