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Home » Choose the correct answer from the given four options in the following questions: The distance between the points (0, 5) and (–5, 0) is (A) 5 (B) 5√2 (C) 2√5 (D) 10
Choose the correct answer from the given four options in the following questions: The distance between the points (0, 5) and (–5, 0) is (A) 5 (B) 5√2 (C) 2√5 (D) 10
CBSE | Class 10 | Coordinate Geometry | Exercise 7.1 | Maths | NCERT Exemplar
Choose the correct answer from the given four options in the following questions: The distance between the points (0, 5) and (–5, 0) is (A) 5 (B) 5√2 (C) 2√5 (D) 10

Solution:

Option (B) 5√ 2 is the correct answer.

Distance formula: {{d}^{2}}~=\text{ }{{({{x}_{2}}~\text{ }{{x}_{1}})}^{2}}~+\text{ }{{({{y}_{2}}~\text{ }{{y}_{1}})}^{2}}

According to the given question,

We have;

{{x}_{1}}~=\text{ }0,\text{ }{{x}_{2}}~=\text{ }\text{ }5

{{y}_{2}}~=\text{ }5,\text{ }{{y}_{2}}~=\text{ }0

{{d}^{2}}~=\text{ }{{\left( \left( \text{ }\text{ }5 \right)\text{ }\text{ }0 \right)}^{2}}~+\text{ }{{\left( 0\text{ }\text{ }5 \right)}^{2}}

d=\text{ }\surd {{\left( -5-0 \right)}^{2}}+\text{ }{{\left( 0-5 \right)}^{2}}

d=\text{ }\surd ({{\left( -5 \right)}^{2}}+\text{ }{{\left( -5 \right)}^{2}})

d\text{ }=~\surd \left( 25\text{ }+\text{ }25 \right)

d=\text{ }\surd 50=\text{ }5\surd 2

As a result, the distance between (0, 5) and ( – 5, 0) = 5√ 2

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