Question

8]. Find the distance between the points 12,3) and (4,1).​

Answer 1

GIVEN :-

• Ponts (12,3) and (4,1).

TO FIND :-

• The distance between them.

SOLUTION :-

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

$: \implies \displaystyle \sf \sqrt{(12 - 4) ^{2} + (3 - 1) ^{2} }$

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

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

$: \implies \displaystyle \sf \sqrt{4(16 + 1)}$

$: \implies \displaystyle \sf \sqrt{4(17)}$

$: \implies\underline{ \boxed{\displaystyle \sf 2\sqrt{17}\: units.}}$

$\therefore \underline {\displaystyle \sf The \ Distance \ between \ the \ points \ is \ 2 \sqrt{17} \ units}$

_____________________

Distance Formula,

$\\ : \implies \displaystyle \sf \sqrt{(x_{2} - x_{1}) ^{2} + ( y_{2} - y_{1}) ^{2} }$

This Formula is used when we have to find the distance between the two points.

Answer 2

Given:

• Points (12,3) and (4,1)

Find:

• Distance between points (12,3) and (4,1)

Solution:

Let, points be P(12,3) and Q(4,1)

Now,

we, know that

$\boxed{\underline{\underline{\rm \to \purple{ PQ = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1}) }^{2} } }}}}$

where,

• $\sf x_1 = 12$
• $\sf x_2 = 4$
• $\sf y_1 = 3$
• $\sf y_2 = 1$

So,

$\rm \implies PQ = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1}) }^{2} }$

$\rm \implies PQ = \sqrt{{(12- 4)}^{2} + {(3- 1) }^{2}}$

$\rm \implies PQ = \sqrt{{(8)}^{2} + {(2) }^{2}}$

$\rm \implies PQ = \sqrt{64 + 4}$

$\rm \implies PQ = \sqrt{68}$

$\rm \implies PQ = \sqrt{4 \times 17}$

$\underline{\boxed{\rm \to PQ = 2\sqrt{17} units}}$

Hence, the distance between the points (12,3) and (4,1) will be 2√17 units