Question

Find the distance between the points R(a+b and a-b) and S(a-b -a -b)
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Answer 1

Answer:

RS = 2√(b² + a²)

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Step-by-step explanation:

According to the question;

R ➝ (a + b, a - b)

S ➝ (a - b, -a - b)

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For any two points with the co-ordinates (x₁, y₁) and (x₂, y₂), the distance formed on joining the two points is given by the Distance formula, which is:

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$\boxed{\sf Distance \ Formula = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

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Where;

• x₁ = a + b

• x₂ = a - b

• y₁ = a - b

• y₂ = -a - b

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Now we'll substitute these values in the distance formula.

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$\sf \dashrightarrow \ Distance \ Formula = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

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Substitute the values;

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$\sf \dashrightarrow \ RS = \sqrt{(a + b - (a - b))^2 + (a - b - (-a - b))^2}$

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$\sf \dashrightarrow \ RS = \sqrt{(a + b - a + b)^2 + (a - b + a + b)^2}$

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$\sf \dashrightarrow \ RS = \sqrt{(b + b)^2 + (a + a)^2}$

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$\sf \dashrightarrow \ RS = \sqrt{(2b)^2 + (2a)^2}$

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$\sf \dashrightarrow \ RS = \sqrt{4b^2 + 4a^2}$

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Take 4 out as common;

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$\sf \dashrightarrow \ RS = \sqrt{4(b^2 + a^2)}$

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$\sf \dashrightarrow \ RS = \sqrt{4} \times \sqrt{(b^2 + a^2)}$

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$\sf \dashrightarrow \ RS = 2\sqrt{(b^2 + a^2)}$

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Therefore the distance between the points R(a + b, a - b) and S(a - b, -a - b) is 2√(b² + a²).