Question

solve the problem...​

Answer 1

Answer :-

• ›»› The distance between the given points is 4√2 or 5.65.

Step-by-step explanation :

Given :-

• A(-5, 7) and B(-1, 3).

To Find :-

• The distance between the given points = ?

Formula required :-

• Formula to calculate the distance between is given by,

→ AB = √{(x₂ - x₁)² + (y₂ - y₁)²}

Here,

• x₂ = -1.
• x₁ = -5.
• y₂ = 3.
• y₁ = 7.

Solution :-

• We know that, if we are given with the x₂, x₁, y₂ and y₁ then we have the required formula, that is,

→ AB = √{(x₂ - x₁)² + (y₂ - y₁)²}

• By using the formula to calculate the distance between and substituting all the given values in the formula, we get :

→ AB = √{(-1 - (-5))² + (3 - 7)²}

→ AB = √{(-1 + 5)² + (3 - 7)²}

→ AB = √{(4)² + (-4)²}

→ AB = √{16 + (-4)²}

→ AB = √(16 + 16)

→ AB = √32

→ AB = 4√2

→ AB ≈ 5.65.

Hence, the distance between the given points is 4√2 or 5.65.

Answer 2

Given:-

• Coordinates of point A = (-5,7)
• Coordinates of point B = (-1,3)

To find:-

• Distance between these two points

Formula to be used:-

$\underline{\boxed{\sf AB = √(x-x')²+(y-y')² }}$

here:-

• X = -5
• X' = -1
• y = 7
• y' = 3

Solution:-

$\longrightarrow$ AB = √(-5-(-1)²+(7-3)²

$\longrightarrow$ AB = √(-5+1)²+(4)²

$\longrightarrow$ AB = √(-4)²+(4)²

$\longrightarrow$ AB = √16+16

$\longrightarrow$ AB = √32 = √2×2×2×2×2

$\longrightarrow$ AB = 4√2 cm.

Additional information:-

To find the coordinates of a point(a,b) which divides a particular line segment in ratio m:n, we use Section Formula =

A = $\sf\dfrac{mx-nx'}{m+n}$

B = $\sf\dfrac{my-ny'}{m+n}$