Co-ordinate geometry

jenny2675 wrote:I want share some my questions.
Determine the distance between them
Find the midpoint, slope and equation of a line segment
Determine if lines are parallel or perpendicular
Find the area and perimeter of a polygon defined by the points
Transform a shape by moving, rotating and reflecting it.
Define the equations of curves, circles and ellipses.

Dear Jenny,

I'm happy to help. That's quite a bit that you ask.

1) distance in the Cartesian plane --- see this blog:
https://magoosh.com/gmat/2012/gmat-coord ... wo-points/

2)Find the midpoint, slope and equation of a line segment
To find the midpoint between two points in the (x, y) plane --- average the two x-coordinates get the x-coordinate of the midpoint, and average the two y-coordinates get the y-coordinate of the midpoint.

To find slope, use the idea that slope = rise/run. Run is the horizontal change, which you find from subtracting the x-coordinates. Rise is the vertical change, which you find by subtracting the y-coordinates. Once you know the rise & run, divide to find the slope.

To find the equation --- once you have the slope, plug that number into y=mx + b, and pick either one of the points (it doesn't matter which one) and plug it's coordinate in for x & y. The deep idea is that every point on the line must satisfy the equation of the line. When you plug in numerical values for m & x & y, you can solve for b --- once you have that, you have the equation of the line.

3) Determine if lines are parallel or perpendicular ----
If two lines have equal slope, they are parallel. The GMAT might expect you to know that.
If the two slopes are opposite reciprocals (like -3 and +1/3, or +3/7 and -7/3), then the lines are perpendicular. Another way to say that, the product of the slopes of perpendicular lines is always -1. This is a relatively rare thing for the GMAT to ask.

4) Find the area and perimeter of a polygon defined by the points
Perimeter is easy --- see the link above in #1 for distance in the Cartesian plane.
Area --- that's a tricky one. For triangles, you should know A = 0.5b*h. You should be able to divide most shapes into rectangles and triangles and find the area that way. The GMAT is NOT going to give you a bizarre set of points and ask you to find the area of the enclosed irregular polygon.
Here's a link to a triangle question:
https://gmat.magoosh.com/questions/813
When you submit your answer, the following screen will have a full video explanation. Each one of our 800+ GMAT questions has its own video explanation, for accelerated learning.

The final two items --- geometric transformations in the Cartesian planes, and equations of curves in general --- those are really the meat & potato of Precalculus, and that's well beyond GMAT math.

Does all this make sense?

Mike

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