Question

Two points A (1,3) and B (4,-6) are given. Find the distance of AB using distance formula.



answer with explanation


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Answer 1

Answer:

3√10 units

Explanation:

Given points,

• A(1, 3)
• B(4, -6)

Using distance formula,

$= \rm \sqrt{ {(x_2 - x_1)}^{2} + {( y_2 - y_1)}^{2} }$

Where,

• $\rm x_1 \: and y_1$ denotes the coordinates of point A.
• $\rm x_2 \: and y_2$ denotes the coordinates of point B.

Substituting the values,

$\rm = \sqrt{ {(4 - 1)}^{2} + {( - 6 - 3)}^{2} }$

$= \sqrt{ {(3)}^{2} + {( - 9)}^{2} }$

$= \sqrt{9 + 81}$

$= \sqrt{90}$

$= 3\sqrt{10}$

Hence, the distance between points A and B is 3√10 units.

Answer 2

Answer:

Given :-

• Two points A(1 , 3) and B(4 , - 6).

To Find :-

• What is the distance of AB by using distance formula.

Formula Used :-

$\bigstar$ Distance Formula :

$\dashrightarrow \sf\boxed{\bold{\pink{Distance =\: \sqrt{\bigg(x_2 - x_1\bigg)^2 + \bigg(y_2 - y_1\bigg)^2}}}}$

where,

• $\sf x_1, y_1$ = Co-ordinates of the first points
• $\sf x_2, y_2$ = Co-ordinates of the second points

Solution :-

Given Points :

$\mapsto \bf A(1 , 3)$

$\mapsto \bf B(4 , - 6)$

where,

• x₁ = 1
• y₁ = 3
• x₂ = 4
• y₂ = - 6

According to the question by using the formula we get,

$\implies \sf AB =\: \sqrt{\bigg(4 - 1\bigg)^2 + \bigg(- 6 - 3\bigg)^2}$

$\implies \sf AB =\: \sqrt{\bigg(3\bigg)^2 + \bigg(- 9\bigg)^2}$

$\implies \sf AB =\: \sqrt{\bigg(3 \times 3\bigg) + \bigg(- 9 \times - 9\bigg)}$

$\implies \sf AB =\: \sqrt{9 + 81}$

$\implies \sf AB =\: \sqrt{90}$

$\implies \sf\bold{\red{AB =\: 3\sqrt{10}}}$

$\therefore$ The distance of AB is 3√10 units .