Question

If the distance between point $P\left(2,2\right)$ and $Q\left(5,x\right)$ is $5$ then the value of $x$ is

• A. $2$
• B. $6$
• C. $3$
• D. $1$

Answer 1

Answer: (B)

$6$

We have,

$P=(2,2),Q=(5,x)$ and $PQ=5$

We know that

$d^2=(x_2-x_1{)}^2+(y_2-y_1{)}^2$

Therefore,

$P{Q}^2=(5-2{)}^2+(x-2{)}^2$

$5^2=(3{)}^2+(x-2{)}^2$

$25=9+(x-2{)}^2$

$(x-2{)}^2=16$

$x-2=\pm 4$

$x=6$ or $x=-2$

Hence, this is the answer.