Question

find the distance between points whose coordinates are P(0,4) and Q(4,0)​

Answer 1

S O L U T I O N :

Let,

• P(0 , 4)
• Q(4, 0)

Applying distance formula,

$\green\bigstar$ Distance between two points = √(x2 - x1)² + (y2 - y1)²

[ Put the values ]

$\implies$ PQ = √(4 - 0)² + (0 - 4)²

$\implies$ PQ = √(4)² + (4)²

$\implies$ PQ = √16 + 16

$\implies$ PQ = √32

$\implies$ PQ = 4√2 units $\red\bigstar$

Therefore,

The distance between P(0,4) and Q(4,0) is 4√2 units.

Answer 2

Given, two points P(0,4) and Q(4,0).

☯we need to find distance between the given points .

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As we know that,

$\star\;{\boxed{\sf{\pink{Distance\;formula = \sqrt{( x_2- x_1)^2 + (y_2 - y_1)^2}}}}}$

Putting values,

$:\implies\sf PQ = \sqrt{(4 - 0)^2 + (0 - 4)^2}$

$:\implies\sf PQ = \sqrt{(4)^2 + (4)^2}$

$:\implies\sf PQ = \sqrt {16 + 16}$

$:\implies\sf PQ = \sqrt {32}$

$:\implies{\boxed{\frak{\purple{ PQ = 4\sqrt 2 \;units }}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\;distance\;between\;PQ\;is\:\bf{ 4\sqrt 2 \;units}.}}}$

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