Question

Find the distance between the points p(-6, 7) Q(-1, -5)

Answer 1

Answer:

13 units

Step-by-step explanation:

PQ = √(-1 +6)² + (-5-7)²

PQ = √(5)² + (-12)²

PQ = √25 + 144

PQ = √169

PQ = 13 units

Answer 2

Given : Two points P (-6,7) and Q (-1,-5).

To Find : Distance between them.

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Here, it is given that, two points are given P and Q. We'll find the distance between these two points using distance formula.

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For finding the distance between the two points, formula is given as :

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$\star\underline{\boxed{\sf\pink{Distance \: formula = \sqrt{(x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} } }}}$

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Here,

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• $\sf \:( x_{1},y_{1} )= ( - 6,7)$
• $\sf \: ( x_{2},y_{2} )= ( - 1, - 5)$

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★ Now, we'll put the values of the co ordinates of P and Q respectively in the formula and find the distance between them.

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$\sf :\implies \: PQ = \sqrt{(x_{2} -x_{1}) {}^{2} +( y_{2} - y_{1}) {}^{2} } \\ \\ \\ \sf :\implies \:PQ = \sqrt{[( - 1) - ( - 6)] {}^{2} + [(- 5) - 7)] {}^{2} } \\ \\ \\ \sf :\implies \:PQ = \sqrt{ [ - 1 + 6] {}^{2} +[ - 5 - 7] {}^{2} } \\ \\ \\ \sf :\implies \: PQ = \sqrt{(5) {}^{2} + ( - 12) {}^{2} } \\ \\ \\ \sf :\implies \: PQ = \sqrt{25 + 144} \\ \\ \\ \sf :\implies \: PQ = \sqrt{169} \\ \\ \\ \sf :\implies \: \underline{\boxed{\mathfrak\purple{PQ = 13 \: units}}} \: \bigstar$

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$\sf\therefore{\underline{Hence, \: the \: distance \: between \: the \: points \: P\: and \: Q\: is \: \bold{13 \: units}.}}$