Question

5.Find the value of Y if the distance between the point A(2, -2) and(-1, y) is 5​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \implies Distance \: between \: the \: point \: A(2,-2) \: and \: B (-1, y) = 5$

$\bf \underline{\underline{\maltese\: To \: find }}$

$\sf \implies Value \: of \: y = \: ?$

$\bf \underline{\underline{\maltese\: Solution }}$

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

$\bf \underline{Where},$

$\sf \implies x_1 = 2$

$\sf \implies x_2 = - 1$

$\sf \implies y_1 = - 2$

$\sf \implies y_2 = \: ?$

$\sf \underline{Putting \: the \: values},$

$\sf \implies \sqrt{(-1-2)^2+(y-(-2))^2} = 5$

$\sf \implies \sqrt{( - 3)^2+(y + 2)^2} = 5$

$\sf \underline{Square \: both \: the \: sides},$

$\sf \implies( - 3)^2+(y + 2)^2= 25$

$\sf \implies9+(y + 2)^2= 25$

$\sf \implies(y + 2)^2= 25 - 9$

$\sf \implies(y + 2)^2= 16$

$\sf \implies y + 2 =\pm \sqrt{16}$

$\sf \implies y + 2 =\pm 4$

$\sf \implies y = 2, -6$

$\underline{\boxed{ \red{\bf Therefore, the \: value \: of \: y \: is -6 \: and \: 2.}}}$