Question

98. find value of P if the distance
between the point A (1,-1) and
B (2,p) is √10

​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given :

• The distance between Point A(1,1) and Point B(2,p) = √10.

To Find :

• The Value of P.

Distance Formula :

$\sf{ \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{10}}$

Here,

$\sf{x_{1} = 1}$

$\sf{x_{2} = 2}$

$\sf{y_{1} = - 1}$

$\sf{ y_{2} = p}$

Substituting the values in the distance formula,

$\sqrt{(2 - 1)^{2} + (p + 1)^{2} } = \sqrt{10}$

Squaring on both sides, to cancel the roots.

$\sf{1 + (p + 1 )^{2} = 10}$

$\sf{1 + {p}^{2} + 2p + 1 = 10}$

$\sf{ {p}^{2} + 2p + 8 = 0}$

Further splitting the middle term,

$\sf{ {p}^{2} + 4p - 2p - 8 = 0}$

$\sf{p(p - 4) - 2(p + 4) = 0}$

$\sf{(p + 4) = 0 \:and \: (p - 2) = 0}$

$\boxed{\sf{ \red{p = - 4}}}$

$\boxed{ \sf{ \blue{p = 2}}}$

So the values of P are -4 and 2.

___________________________________