Question

Question 19
If the distance between the points (4,p) and (1,0) is 5, then the value of p is
(A) $4only$
(B) $\pm 4$
(C) $-4only$
(D) $0$

Answer 1

According to the question, the distance between the points (4,p) and (1,0) = 5
$\Rightarrow$ $\sqrt{(1-4{)}^2+(0-p{)}^2}=5\left[\begin{array}{c}\because \text{Distance between two points two points}(x_1,y_1)and(x_2,y_2),d\\ =\sqrt{(x_2-x_1{)}^2+(x_2-y_1{)}^2}\end{array}\right]\Rightarrow \sqrt{(-3{)}^2+p^2=5}\Rightarrow \sqrt{9+p^2}=5\text{On squaring both the sides, we get}9+p^2=25\Rightarrow p^2=16\Rightarrow p=\pm 4\text{Hence, the required value of p is}\pm 4$