What is the formula to find distance in coordinate geometry, given coordinates (x_1, y_1), (x_2, y_2)? (valid variables for this problem: x_1, x_2, y_1, y_2)

The distance formula is:

Step-by-step explanation:

Given:

Two points on a coordinate plane are given as:

Now, let the points be and let 'd' be the distance between the two points.

Now, join the points A and B to make a line segment AB.

Also, draw a right angled triangle ABC right angled at point C. Point C is is the intersection of horizontal and vertical lines drawn from points A and B respectively as shown in the figure below.

From the triangle ABC, we observe that:

AB =

AC =

BC =

Now, we use Pythagoras theorem to find 'd'. This gives,

Now, taking square root on both sides, we get:

Ignoring the negative result as distance can never be negative.

Therefore, the formula  to find distance in coordinate geometry, given coordinates is: