Question

Assertion (A): The distance of P (a, b) from origin is a² + b².

Reason (R): The distance between two points `A(x_1, y_1) and B(x_2, y_2)` is `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:

Assertion (A): The distance of P(a, b) from origin, i.e., (0, 0), is given by the distance formula,

`sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

where (x₁, y₁) and (x₂, y₂) are two points on a plane.

Here, (x₁, y₁) = (a, b) and (x₂, y₂) = (0, 0)

On substituting the values in the formula, we get

`sqrt((0 - a)^2 + (0 - b)^2)`

= `sqrt(a^2 + b^2)`

Therefore, assertion (A) is true.

Reason (R): The distance between the points A(x₁, y₁) and B(x₂, y₂) is given by the distance formula,

`sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Therefore, Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true. Also, Reason (R) is the correct explanation of Assertion (A).