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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
Let $A=\left(a_1, a_2\right)$ and $B=\left(b_1, b_2\right)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$ ?
  • A
    $\sqrt{65}$
  • B
    $\sqrt{7} \overline{4}$
  • ✓
    $\sqrt{8 \overline{3}}$
  • D
    $\sqrt{9} \overline{7}$
✓

Answer

Correct option: C.
$\sqrt{8 \overline{3}}$
c
(c)

Given,

$A=\left( a _1, a_2\right), B=\left(b_1, b_2\right)$, where $a_1, a_2, b_1, b_2$ are integers.

Distance between $A B$

$=\sqrt{\left(b_1-a_1\right)^2+\left(b_2-a_2\right)^2}$

$\therefore A B=\sqrt{\text { sum of squares of two number }}$

$\sqrt{65}=\sqrt{64+1}$, it is possible.

$\sqrt{74}=\overline{\sqrt{49+2}}$, it is also possible.

$\sqrt{97}=\sqrt{81+16}$, it is also possible.

$83$ is not a sum of squares of two number.

Hence, option $(c)$ is correct.

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