Question

The distance between points (4,3) and (2,-5) is

a) 2√17
b) 68
c) √18
d) 2√17 and -2√17

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Answer 1

Given:

• Points are (4,3) and (2,-5)

Find:

• Distance between the points ?

Solution:

Here,

Let, the given points be A(4,3) and B(2,-5)

Now,

we, know that

$\underline{ \boxed{ \orange{ \sf AB = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} }}}}$

where,

• $\sf x_1$ = 4
• $\sf x_2$ = 2
• $\sf y_1$ = 3
• $\sf y_2$ = -5

Now,

$\sf \to AB = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

$\sf \to AB = \sqrt{{(2 - 4)}^{2} + {( - 5- 3)}^{2}}$

$\sf \to AB = \sqrt{{( - 2)}^{2} + {( - 8)}^{2}}$

$\sf \to AB = \sqrt{4 + 64}$

$\sf \to AB = \sqrt{68}$

$\sf \to AB = \sqrt{17 \times 4}$

$\underline{ \boxed{ \green{\sf \to AB = </strong><strong>±</strong><strong> </strong><strong>2\sqrt{17}}}}$

Hence, the distance between the points A(4,3) and B(2,-5) are 2√17 and -2√17

So, the option will be d) 2√17 and -2√17

Answer 2

GIVEN :-

• Points (4,3) and (2,-5).

TO FIND :-

• The distance between them.

SOLUTION :-

$\\ : \implies \displaystyle \sf \sqrt{(x _{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} } \: \: \: \: \: \: \: \: \bigg \lgroup Distance Formula \bigg \rgroup$

$: \implies \displaystyle \sf \sqrt{(4 - 2) ^{2} + (3 - ( - 5)) ^{2} }$

$: \implies \displaystyle \sf \sqrt{(2) ^{2} + (3 + 5) ^{2} }$

$: \implies \displaystyle \sf \sqrt{4 + (8) ^{2} }$

$: \implies \displaystyle \sf \sqrt{4 + 64}$

$: \implies \displaystyle \sf \sqrt{68}$

$: \implies \underline{ \boxed{\displaystyle \sf \pm \: 2\sqrt{17} }} \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \displaystyle \sf \: Distance \bigg \rgroup$

$\therefore \underline{\displaystyle \sf Distance \: between \: (4,3) \: and \: (2,-5) \: is \: 2 \sqrt{17} \: and \: -2\sqrt{17}}$

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$\\ \\ \displaystyle \sf Distance \ Formula = \sqrt{(x _{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }$