# Find that value(s) of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.

It is known that the distance between the points $\left({x}_{1},{y}_{1}\right),\left({x}_{2},{y}_{2}\right)$
is $\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}$

According to question,

$PQ=10=\sqrt{{\left(x-9\right)}^{2}+{\left(4-10\right)}^{2}}\phantom{\rule{0ex}{0ex}}⇒{\left(x-9\right)}^{2}+36=100\phantom{\rule{0ex}{0ex}}⇒{\left(x-9\right)}^{2}=64\phantom{\rule{0ex}{0ex}}⇒{x}^{2}+81-18x-64=0\phantom{\rule{0ex}{0ex}}⇒{x}^{2}-18x+17=0\phantom{\rule{0ex}{0ex}}⇒{x}^{2}-17x-x+17=0\phantom{\rule{0ex}{0ex}}⇒x\left(x-17\right)-\left(x-17\right)=0\phantom{\rule{0ex}{0ex}}⇒\left(x-1\right)\left(x-17\right)=0\phantom{\rule{0ex}{0ex}}⇒x=1,17$

Hence, the required values of x will be 1 and 17.

• 0

(PQ)2 = 102 =  100

(9-x)2 + (10-4)2 = 100

81 - x2 - 18x  + 36 = 100

x2 - 18x + 17 = 0

by splitting the middle term

(x-1)(x-18)

• 1
sorry it was left incomplete then we get x=1 or x= 18
• 2
What are you looking for?