Question

Given the coordinates of two points in the plane you can can use either the distance formula of the Pythagorean theorem to find the distance between them

Answer 1

Given:

The coordinates of two points in the plane are given.

Then to find the distance between the two points is given by distance formula.

Also, the distance formula is derived from the Pythagorean theorem.

Step-by-step explanation:

Let The two points in the plane have coordinates (x1, y1) and (x2,y2).

Draw a right angled triangle whose hypotenuse joins the two points.

Then the adjacent side has a length of x2 - x1.

The opposite side has a length of y2 - y1.

Let d be the length of the hypotenuse.

Using Pythagorean theorem, we have:

`\begin{gathered} d^2=(x2-x1)^2+(y2-y1)^2 \\ d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \end{gathered}`

hence, distance formula is derived from Pythaogorean theorem.

Therefore, the given statement is true.

Hence first option : True is correct.