Question

If the distance between the two points A(3,p) and B(-5,1) is √65 units. Find p.
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Answer 1

Answer:

• p = 0

Explanation:

Given points,

• A(3, p)
• B(-5, 1)

Distance between A and B is √65 units.

Find the value of p.

Using distance formula,

$\boldsymbol{ \bullet \: \: \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }$

Where,

• $\boldsymbol {x_1, \: y_1}$ are the coordinates of A.
• $\boldsymbol {x_2, \:y_2}$ are the coordinates of B.

Substitute the given coordinates,

${ \implies \sqrt{65} \: = \sqrt{ {[( - 5) - 3]}^{2} + {(1 - p)}^{2} } }$

On squaring both sides,

${ \implies {65} \: = { {[ - 5- 3]}^{2} + {(1 - p)}^{2} } }$

${ \implies {65} \: = { {[ - 8]}^{2} + {(1 - p)}^{2} } }$

${ \implies {65} \: = {64 + {(1 - p)}^{2} } }$

${ \implies {65} - {64 = {(1 - p)}^{2} } }$

${ \implies 1 = {(1 - p)}^{2} }$

On ‘√’ both sides,

${ \implies 1 = 1 - p}$

$\implies p = 1 - 1$

$\therefore \boldsymbol{ p = 0}$

∴ The value of ‘p’ is 0