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stiks02 [169]
3 years ago
13

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)

Mathematics
1 answer:
madreJ [45]3 years ago
4 0

Answer:

The distance formula is: d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step-by-step explanation:

Given:

Two points on a coordinate plane are given as:

(x_1,y_1)\ and\ (x_2,y_2)

Now, let the points be A(x_1,y_1)\ and\ B(x_2,y_2) 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 = d

AC = x_2-x_1

BC = y_2-y_1

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

AB^2=AC^2+BC^2\\\\d^2=(x_2-x_1)^2+(y_2-y_1)^2

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

\sqrt{d^2}=\pm\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Ignoring the negative result as distance can never be negative.

Therefore, the formula  to find distance in coordinate geometry, given coordinates (x_1, y_1), (x_2, y_2) is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

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