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Mathematics

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 = (4)2+(3)2\sqrt{(-4)^2 + (3)^2}.

  1. Both the statements are true.

  2. Both the statements are false.

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

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

Distance Formula

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Answer

For the point P, x = -4 and y = 3, the distance of P from origin is 3 + 4 = 7. Distance Formula, Concise Mathematics Solutions ICSE Class 9.

Given, point P, x = -4 and y = 3.

Using distance formula,

Distance between points = (x2x1)2+(y2y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

Distance of P(-4, 3) from origin (0, 0)

=(0(4))2+(03)2=42+(3)2=16+9=25=5 units.= \sqrt{(0 - (-4))^2 + (0 - 3)^2}\\[1em] = \sqrt{4^2 + (-3)^2}\\[1em] = \sqrt{16 + 9}\\[1em] = \sqrt{25}\\[1em] = 5 \text{ units}.

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

Hence, option 4 is the correct option.

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