Question

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

Answer 1

here is your answer.........
hope uit will help you .......
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Answer 2

The value of p is +4 or -4

Solution:

We have been given that the distance between the points (4,p)and (1,0) is 5  

We need to find the value of p.

To find the distance between 2 points we use the formula

$\text{ Distance between the points } =\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

$\text{ Where } x_2=1, y_2=0,x_1 = 4 \text{ and } y_1 = p$

Therefore we can write the formula as follows:

$\begin{aligned}&5=\sqrt{(1-4)^{2}+(0-p)^{2}}\\\\&5=\sqrt{(3)^{2}+(p)^{2}}\end{aligned}$

By squaring on both sides we get:

$\begin{aligned}&25=3^{2}+p^{2}\\\\&p^{2}=25-9\\\\&p^{2}=16\\\\&p=\sqrt{16}\\\\&p=+4 \text{ or } -4\end{aligned}$

Therefore, the value of p is +4 or -4

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