Co-ordinate Geometry is the third most liked topics of GRE. Usually the questions asked in coordinate geometry holds high weightage and because of that a single right solution of this topic can benefit you a lot. So, let us check the basic concepts of coordinate geometry and tackle it on D-day with full confidence.
Two perpendicular real number lines that intersect each other at their respective zero points defines the rectangular coordinate system, which is commonly known as the x and y- coordinate plane or xy plane. In the x and y plane, the horizontal line is known as the x- axis, whereas, the vertical line is y- axis. The point where these two lines intersect is known as the origin, and it is denoted by O. In the x- axis, the values represented on the right of zero are positive values, whereas, values on the left of zero are negative values. Meanwhile, the y- axis is also divided into positive and negative segment. The first half of y- axis that are represented above 0 are positive whereas points below zero are negative.
These perpendicular intersecting lines divides the plane into four quadrants, which can be represented as –
In this figure,
- The values in the first quadrant, both x and y, are positive
- The values in the second quadrant, y is positive whereas x is negative.
- The values in the third quadrant, both x and y is negative.
- The values in the fourth quadrant, x is positive whereas y is negative.
Representation is x, y- coordinates:
The value is represented inside a bracket where the first value represents the x-coordinate and second value represents the y-coordinate.
The representation of values in all four quadrants is as follows:
- (x, y) ← First quadrant
- (-x, y) ← Second quadrant
- (-x, -y) ← Third Quadrant
- (x, -y) ← Fourth quadrant
Let’s solve a problem to understand it in details.
Question: Here, lines i and l are parallel
Find the value of y.
Solution: By using the complementary and supplementary rules of geometry, as the lines i and l are parallel to one another and the sum of all angles of a triangle is 180°.
So, step1. 180° – 125° = 55°
Step 2: 55° + 90° + x = 180°
Step3: x = 35°
Step4: x + y = 180°
35° + y = 180°
y = 145°