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If the point A(0, 2) is equidistant from the points B(3, p) an

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If the point $A (0, 2)$ is equidistant from the points $B (3, p)$ and $C (p, 5)$ , find the value of p. Also, find the length of AB.

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Michael Discussed

If the point

A (0, 2)

is equidistant from the points

B (3, p)

and

C (p, 5)

, find the value of p. Also, find the length of AB.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Given:

A (0, 2)

is equidistance from

B (3, p)

and

C (p, 5)

which implies:

A B = A C

A B^{2} = A C^{2}

Using distance formula:
Distance formula:

PQ = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

We have,

(3 - 0)^{2} + (p - 2)^{2} = (p - 0)^{2} + (5 - 2)^{2}

(3)^{2} + (p - 2)^{2} = p^{2} + (3)^{2}

p^{2} = p^{2} - 4 p + 4

4 p = 4

\Rightarrow p = \frac{4}{4} = 1

and

A B = (3 - 0)^{2} + (1 - 2)^{2}

= 9 + 1 = 10

units.

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Question Text	If the point $A (0, 2)$ is equidistant from the points $B (3, p)$ and $C (p, 5)$ , find the value of p. Also, find the length of AB.
Answer Type	Text solution:1
Upvotes	150