Answer

Verified

413.1k+ views

**Hint:**We will use the distance formula $d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $ where the two points are $({x_1},{y_1})$ and $({x_2},{y_2})$ and thus equated with the given four options and thus, we will get our answer.

**Complete step-by-step answer:**

Let us first discuss the distance formula:-

Let the two points be $({x_1},{y_1})$ and $({x_2},{y_2})$. So, the distance d between between the given two points are given by: $d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $. This distance is known as Euclidean distance. This is an application of Pythagorean Theorem.

The Pythagorean Theorem consists of a formula ${a^2} + {b^2} = {c^2}$ which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the two "non-hypotenuse" sides of the triangle (Opposite and Adjacent).

So, if we compare the two given points (2, 3) and (-4, 5) with $({x_1},{y_1})$ and $({x_2},{y_2})$, we will have:-

${x_1} = 2$, ${y_1} = 3$, ${x_2} = - 4$ and ${y_2} = 5$.

Putting all these values in the mentioned distance formula that is $d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $.

So, we will get the following expression:

$d = \sqrt {{{( - 4 - 2)}^2} + {{(5 - 3)}^2}} $

$\therefore d = \sqrt {{{( - 6)}^2} + {{(2)}^2}} $

$\therefore d = \sqrt {36 + 4} $

$\therefore d = \sqrt {40} $

There is no such option.

So, we will simplify the number inside the root more to get the desired value.

$40 = 2 \times 2 \times 2 \times 5$

Therefore, $\sqrt {40} = \sqrt {2 \times 2 \times 2 \times 5} = 2 \times \sqrt {2 \times 5} $.

Hence, $d = 2\sqrt {10} $.

**So, the correct answer is “Option B”.**

**Note:**Students must note that even if you interchange the points in the distance formula, it would not affect the result which says that if two points are A and B, then AB = BA. This is happening because we are eventually squaring the difference of terms which will neglect – sign.

Sometimes, it is also possible that you may have the option of without simplified value inside the root and after simplifying, we would not be able to match it to any option. So, always remember to check the earlier result before you simplify.

Fun Fact:- There are a lot of types of differences in real numbers only. There is even one which is known as Taxi-Cab distance.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Which are the Top 10 Largest Countries of the World?

The provincial president of the constituent assembly class 11 social science CBSE

Write the 6 fundamental rights of India and explain in detail