Question

If a point A(0,2) os equidistant from the points B(3,p) and C(p,5), then find the value of 'p'.

Answer 1

Since A is equidistant frm B & C, we can say AC = BC

Answer 2

${\huge{ \boxed{\color{teal}{\textsf{\textbf{Answer:}}}}}}$

To Solve:

If point A (0,2) is equidistant from the point B (3, p)and C (p, 5), find p

Solⁿ:

Mid Point - A•(0,2)

Equidistant 1 - B•(3,p)

Equidistant 2 - C•(p,5)

AB = BC (distance)

Distance Formula :

$\sqrt{ { ({x}^{2} - {x}^{1} )}^{2} + { ({y}^{2} - {y}^{1} )}^{2}}$

A• x = 0 , y = 2

B• x = 3 , y = p

C• x = p , y = 5

${ \tt{ \sqrt { {(3 - 0)}^{2}+{(p - 2)}^{2} } = \sqrt{ {(p - 0)}^{2} + {(5 - 2)}^{2} }}} \\ \\ { \tt{\sqrt{9 + {p}^{2} + 4 - 4p } = \sqrt{ {p}^{2} + 9 }}} \\ \\ { \tt{ \red{squaring \: \: both \: \: the \: \: sides}}} \\ \\ { \tt{9 + {\cancel{{p}^{2}}} + 4 - 4p \: \: = \: \: {\cancel{{p}^{2}}} + 9}} \\ \\ { \tt{13 - 9 = 4p}} \\ \\ { \tt{4 = 4p}} \\ \\ { \tt{\frac{4}{4} = p}} \\ \\ { \boxed{ \tt{ \blue{1 = p}}}}$

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