Question

Statement (1): For the point P, 𝑥 = −4 and 𝑦 = 3, the distance of P from origin is 3 + 4 = 7.

Statement (2): P = (−4, 3) and its distance from origin \[= \sqrt{(-4)^2 + (3)^2}\].

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

• Statement (1): Distance in a coordinate plane is Euclidean straight-line distance given by \(\sqrt{x^2 + y^2}\), not the arithmetic sum of the coordinates. For P(-4, 3), the actual distance from the origin is \[\sqrt{(-4)^2 + 3^2} = \sqrt{16 + 9} = 5\text{ units}\], not 7. Hence, Statement (1) is false.
• Statement (2): By the distance formula, the distance of any point (x, y) from the origin (0, 0) is \[\sqrt{(x - 0)^2 + (y - 0)^2} = \sqrt{x^2 + y^2}\]. For P(-4, 3), this is correctly written as \[\sqrt{(-4)^2 + (3)^2} = 5\]. Hence, Statement (2) is true.