Cartesian System of Rectangular Co-Ordinates, Quardrants, Distance Between Two Points

Get unlimited access to the best preparation resource for SAT Mathematics: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 145K)

Quardrants

We know that coordinate axes and divide the region of the plane into four regions. These regions are called the quardrants as shown in Fig. In accordance with the convention of signs, for a point in different quadrants, we have

Point P(x,y) in different quadrants

Point P(X,Y) in Different Quadrants

Point P(x,y) in different quadrants

I quadrant:

II quadrant:

III quadrant:

IV quadrant:

Distance between Two Points

Recall that you have derived the distance formula between two points and in the following manner:

Let us draw a line through. Let be the point of intersection of the perpendicular from to the line. Then is a right-angled triangle.

Distance Between Two Points

Distance between Two Points

Distance Between Two Points

Also

And

Now (Pythagoras theorem)

Example:

Find the distance between the following pairs of points:

(1) and (2) and

Solution:

(1) Distance between two points

Here

Distance between and

Distance between and is units.

(2) Here

Distance between and

Distance between and is units

Developed by: