Question

...... ..............​

Answer 1

Answer:

The right option is..A

Hope it helps

Mark me as brainliest

Answer 2

$\setlength{ \unitlength}{1cm} \thicklines} \begin{picture}(10,10) \put(0,0){ \line(1,0){6.5}} \put(1, - 0.25){ \line(0,1){0.5}} \put(0.9,0.5){ \sf A } \put( 0.6, - 0.5){ \sf (5, a)} \put(5.5, - 0.25){ \line(0,1){0.5}} \put(5.4,0.5){ \sf B} \put(5.1, - 0.5){ \sf (2, 0)} \end{picture}$

Given, Distance between the points A and B is 5 units.

We know,

Distance Formula:

$\qquad \sf Distance = \sqrt{( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2} }$

Point A : x1 = 5, y1 = a

Point B : x2 = 2, y2 = 0

Given, Distance = 5 units

Substituting values,

$\rightarrow \qquad \sf \sqrt{(2 - 5) ^{2} + {(0 - a)}^{2} } = 5 \\ \\ \rightarrow \qquad \sf \sqrt{ {( - 3)}^{2} + {( - a)}^{2} } = 5 \\ \\ \rightarrow \qquad \sf \sqrt{9 + {a}^{2} } = 5 \\ \\ \sf Square \: both \: sides \\ \\ \rightarrow \qquad \sf 9 + {a}^{2} = {(5)}^{2} \\ \\ \rightarrow \qquad \sf {a}^{2} = 25 - 9 \\ \\ \rightarrow \qquad \sf a = \pm \: 4$

Hence, Value of a is ± 4

So, Option A is correct.