Question

Find the distance between the point P (a+b,a-b)
and Q (a-b, a+b)​

Answer 1

Answer:

• 2b√2 units

Explanation:

Given points,

• P(a+b, a-b)
• Q(a-b, a+b)

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 P
• $\rm x_2 \: and \: y_2$ denotes the coordinates of Q

Substituting the given coordinates,

${ = \rm \sqrt{ { \big[(a - b) - (a + b) \big]}^{2} + { \big[(a + b) - (a - b) \big]}^{2} } }$

${ = \rm \sqrt{ { \big[a - b - a - b \big]}^{2} + { \big[a + b - a + b \big]}^{2} } }$

${ = \rm \sqrt{ { \big[ - 2b \big]}^{2} + { \big[2b\big]}^{2} } }$

$\rm = \sqrt{4 {b}^{2} + {4b}^{2} }$

$\rm = \sqrt{ {8b}^{2} }$

$\rm = 2b\sqrt{ {2}}$

Hence, the distance between P and Q is 2b√2 units.

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Formula used,

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

Where,

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

Answer 2

Given :

• P(a+b, a-b)
• Q(a-b, a+b)

To find :

• Distance of the point.

Distance formula

• $\sf\sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2}}$

Solution :

$\sf \: PQ = \sqrt{((a - b) - (a + b)) {}^{2} + ((a - b) - (a - b)) {}^{2} }$

= 4b² + 4b²

$\sf = \sqrt{8b {}^{2} }$

$\red{ \sf \: = 2b \: \sqrt{2} \: units}$