Question

Find the distance between the following
(ii) A(-5, -1) and B(0, 4)

Answer 1

Answer:

A(-5, -1) and B(0, 4)

(-5,-1)=(x_1,y_1)

(0,4)=(x_2,y_2)

FORMULA

√(x_2-x_1)^2+(y_2-y_1)^2

PUT THE VALUE IN THIS FORMULA

√(0+5)^2+(4+1)^2

√(5)^2+(5)^2

√25+25

√50

√25×2

5√2

Answer 2

Given :

• A(-5, -1)
• B(0, 4)

To Find :

The distance between them.

Solution :

Analysis :

Here we have to use the distance formula to solve the sum.

Required Formula :

Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]

where,

• (x₁, y₁) = Coordinates of first point
• (x₂, y₂) = Coordinates of second point

Explanation :

• A(-5, -1)
• B(0, 4)

We know that if we are given the coordinates of the two points and is asked to find the distance then our required formula is,

Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]

where,

• x₁ = -5
• x₂ = 0
• y₁ = -1
• y₂ = 4

Using the required formula and substituting the required values,

⇒ Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]

⇒ Distance = √[(0 – (-5))² + (4 – (-1))²]

⇒ Distance = √[(0 + 5)² + (4 + 1)²]

⇒ Distance = √[(5)² + (5)²]

⇒ Distance = √[25 + 25]

⇒ Distance = √[50]

⇒ Distance = 5√2

∴ Distance = 5√2 units.

The distance between the points is 5√2 units.

Explore More :

Mid–Point Formula :

$\bf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Section Formula :

$\bf (x,y)=\left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$

Centroid of Triangle :

$\bf (x,y)=\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)$