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:

step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.

the one below it is a function