Question

What is the distance between the 2 coordinate points a(6,-4) and b(12,4)?

Answer 1

Answer:

(6 -,4) =10 and (12,4)=8 units

Answer 2

$\huge \fcolorbox{green}{red}{ \bf \purple{10 \: units}}$

Step-by-step explanation:

Q.

What is the distance between the 2 coordinate points a(6, - 4) and b(12, 4) ?

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SOLUTION :-

Here,

$\bf x_{1},y_{1} = 6 ,- 4 \\ \bf = > x_{1} = 6 ,y_{1} = - 4 \\ \\ \bf x_{2},y_{2} = 12,4 \\ = > \bf x_{2} = 12,y_{2} = 4$

To find the distance, we use formula -

$\bf \large\sqrt{(x_{2} - x_{1} {)}^{2} + (y_{2} - y_{1} {)}^{2} } \\ \\ \bf = > \sqrt{ (12 - 6 {)}^{2} + \{4 - ( - 4) { \}}^{2} } \\ \\ \bf = > \sqrt{ {6}^{2} + (4 - 4 {)}^{2} } \\ \\ \bf = > \sqrt{36 + {8}^{2} } \\ \\ \bf = > \sqrt{36 + 64} \\ \\ \bf = > \sqrt{100} \\ \\ \bf = > \sqrt{ {10}^{2} } \\ \\ \bf = > \purple{10 \: units}$

So,

the distance between points A and B is 10 units.

Note :-

The formula can be written in two forms -

$\bf i) \sqrt{(x_{1} - x_{2} {)}^{2} + (y_{1} - y_{2}} \\ \bf ii) \sqrt{(x_{2} - x_{1}) + (y_{2} - y_{1}}$

Both are correct and will give you same answer.

Hope it helps.