Co-ordinate Geometry — Important Questions

Distance is always positive, It's based on Pythagoras theorem, Distance from origin to point (3,4) is 5, Formula is d = √[(x₂-x₁)² + (y₂-y₁)²]

Distance is always positive (absolute value), based on Pythagoras theorem. Distance from (0,0) to (3,4) = √(3²+4²) = 5. The standard formula is correctly stated.

(3, 2)

Using centroid formula: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3) = ((0+6+3)/3, (0+0+6)/3) = (9/3, 6/3) = (3, 2)

13

Using distance formula: d = √[(5-0)² + (12-0)²] = √[25 + 144] = √169 = 13. This is a 5-12-13 Pythagorean triplet.