Question

If the distance between the points (4,p)and(1,0) is 5 find the value of p is

Answer 1

$\purple{ \underline{ \huge \fbox{ \mathtt{ \orange{ \: Solution : \: \: }}}}}$

Given ,

The points are (4,P) and (1,0)

The distance between (4,P) and (1,0) points is 5 units

We know that , the distance between the two points are given by

$\mathtt{ \fbox{Distance = \sqrt{ { (x_{2} - x_{1} )}^{2} + {(y_{2} - y_{2} )}^{2} } } \: \: \: \: \: \: \: \: }$

Substitute the values , we obtain

$\sf \hookrightarrow {5 = \sqrt{ {(1 - 4)}^{2} + {(0 - p)}^{2} } }$

On squaring both sides , we get

$\sf \hookrightarrow 25 = {( - 3)}^{2} + {( - p)}^{2} \\ \\ \sf \hookrightarrow 25 = 9 + {(p)}^{2} \\ \\ \sf \hookrightarrow p = \sqrt{16} \\ \\ \sf \hookrightarrow p = 4$

Hence , the value of P is 4