Question

How do you use the Pythagorean theorem to find the distance between two points like the points (1,3) and (4,3) ?

Answer 1

Hint: In order to solve this question, we first have to take the given points as the 2 sides of the right angled triangle such that the two points form the hypotenuse. Then you have to use the Pythagorean theorem to find the length of the hypotenuse. This length is the distance between the two points.

Complete step by step solution:
According to the problem, we are asked to use the Pythagorean theorem to find the distance between two points like the points (1,3) and (4,3).
For this, we first have to take the given points as the 2 sides of the right angled triangle such that the two points form the hypotenuse. Then you have to use the Pythagorean theorem to find the length of the hypotenuse. This length is the distance between the two points. Then we get our final answer.
Here, first we take the values as
$\left( 1,3 \right)=\left( a,b \right)$ , $\left( 4,3 \right)=\left( c,d \right)$ and $origin=\left( 0,0 \right)$.
Now we take them as the points which connect hypotenuses. Then after using the Pythagorean theorem, we get:
$ \Rightarrow {{\left( a-c \right)}^{2}}+{{\left( b-d \right)}^{2}}={{l}^{2}}$
$ \Rightarrow {{\left( 1-4 \right)}^{2}}+{{\left( 3-3 \right)}^{2}}={{l}^{2}}$
$ \Rightarrow 9={{l}^{2}}$
$ \Rightarrow l=3$-
Here, we got the distance between the two points as 3.
Therefore, after all the solving, we get the final answer that is the distance between the two points as 3.

Note: In order to solve this question, you have to know the Pythagorean theorem. Without knowing it, you cannot do this. You also have to be careful while substituting the values in the equations. You have to subtract x coordinate with x coordinate only.