Question

find the distance between the
following point.
i]A(a,0),B(0,a)
ii]P(-6,-3),Q(-1,9)
iii]R(-3a,a),S(a,-2a)​

Answer 1

Answer:

i. Let A (x1 , y1 ) and B (x2 , y2 ) be the given points. ∴ x1 = a, y1 = 0, x2 = 0, y2 = a By distance formula, ∴ d(A, B) = a√2 units

ii. Let P (x1 , y1 ) and Q (x2 , y2 ) be the given points. ∴ x1 = -6, y1 = -3, x2 = -1, y2 = 9 By distance formula, ∴ d(P, Q) = 13 units

iii. Let R (x1 , y1 ) and S (x2 , y2 ) be the given points. ∴ x1 = -3a, y1 = a, x2 = a, y2 = -2a By distance formula, ∴ d(R, S) = 5a units

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Answer 2

Step-by-step explanation:

distance between two points

$d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }$

I. AB=

$\sqrt{(0 - a) {}^{2} + (a - 0) {}^{2}} \\ = \sqrt{( - a) {}^{2} + (a) {}^{2}} = a\sqrt{2}$

2. PQ=

$\sqrt{( - 1 + 6) {}^{2} + (9 + 3) {}^{2}} \\ = \sqrt{(5) {}^{2} +(12{)}^{2}} \\ = \sqrt{25 + 144} = \sqrt{169} \\ = 13$

3. RS=

$\sqrt{(a + 3a) {}^{2} + ( - 2a - a) {}^{2} } \\ = \sqrt{(4a) {}^{2} + ( - 3a) {}^{2} } \\ = \sqrt{8a {}^{2} + 9a {}^{2}} = \sqrt{17a {}^{2} } \\ = a \sqrt{17}$