Question

Consider the following points :
1. (0, 5)
2. (2, -1)
3. (3, -4) Which of the above be on the line $3x+y=5$ and at a distance $\sqrt{10}$ from (1, 2)?

• A. 1 only
• B. 2 only
• C. 1 and 2 only
• D. 1, 2 and 3

Answer 1

The correct option is C 1 and 2 only

first check if the points lie on the line 3x+y=5

$i\left)\right(0,5\left)3\right(0)+5=5$

$\Rightarrow$ the point lies on the line

$ii\left)\right(2,-1\left)3\right(2)-1=5$

$\Rightarrow$ This point also lies on the line

$iii\left)\right(3,-4\left)3\right(3)-4=5$

$\Rightarrow$This point also lies on the line

$nowcheckfordistancefrompoint(1,2)i)d=\sqrt{{(0-1)}^2+{(5-2)}^2}=\sqrt{10}ii)d=\sqrt{{(2-1)}^2+{(-1-2)}^2}=\sqrt{10}iii)d=\sqrt{{(3-1)}^2+{(-4-2)}^2}=\sqrt{40}$

Only 1 and 2 lie at a distance of $\sqrt{10}$ from point (1,2).