Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Find the distance between $A\left( {a + b,b - a} \right)$ and $B\left( {a - b,a + b} \right)$?

Last updated date: 20th Jun 2024
Total views: 441.9k
Views today: 8.41k
Verified
441.9k+ views
Hint: In this question we will use distance formula to find the distance between two points. Distance formula, $d = \sqrt {{{\left( {{x_1} - {x_2}} \right)}^2} + {{\left( {{y_1} - {y_2}} \right)}^2}}$.

$A\left( {a + b,b - a} \right)$ and $B\left( {a - b,a + b} \right)$
Distance Formula: The distance formula is used to determine the distance, $d$ , between two points. If the coordinates of the two points are $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$, the distance equals the square root of $\left( {{x_1} - {x_2}} \right)$ squared $+ \left( {{y_1} - {y_2}} \right)$ squared.
$d = \sqrt {{{\left( {{x_1} - {x_2}} \right)}^2} + {{\left( {{y_1} - {y_2}} \right)}^2}}$
Now, the distance between $A$ and$B$ is determined by using the distance formula.
$\Rightarrow {\text{ }}AB = \sqrt {{{\left( {\left( {a + b} \right) - \left( {a - b} \right)} \right)}^2} + {{\left( {\left( {b - a} \right) - \left( {a + b} \right)} \right)}^2}} \\ {\text{or }}AB = \sqrt {{{\left( {a + b - a + b} \right)}^2} + {{\left( {b - a - a - b} \right)}^2}} \\ {\text{or }}AB = \sqrt {{{\left( {2b} \right)}^2} + {{\left( { - 2a} \right)}^2}} \\ {\text{or }}AB = \sqrt {4{b^2} + 4{a^2}} \\ {\text{or }}AB = \sqrt {4\left( {{a^2} + {b^2}} \right)} \\ {\text{or }}AB = 2\sqrt {\left( {{a^2} + {b^2}} \right)} \\$
Thus the distance between $A\left( {a + b,b - a} \right)$ and $B\left( {a - b,a + b} \right)$$= 2\sqrt {\left( {{a^2} + {b^2}} \right)}$
Note: These types of questions can be solved by using distance formulas. In this question, we simply apply the distance formula between the given point and we get the distance between the points $A{\text{ and }}B$.