Coordinate Geometry

Answer

Step 1: Apply distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] Step 2: Substitute values: d = √[(7-3)² + (1-4)²] Step 3: Simplify: d = √[4² + (-3)²] = √[16 + 9] Step 4: Calculate: d = √25 = 5 units Answer

Answer

Step 1: Find all side lengths using distance formula PQ = √[(4-1)² + (2-7)²] = √[9+25] = √34 QR = √[(-1-4)² + (-1-2)²] = √[25+9] = √34 RS = √[(-4-(-1))² + (4-(-1))²] = √[9+25] = √34 SP = √[(1-(-4))² +

Answer

Step 1: Apply section formula: P(x,y) = [(m₁x₂ + m₂x₁)/(m₁+m₂), (m₁y₂ + m₂y₁)/(m₁+m₂)] Step 2: Here m₁:m₂ = 2:1, A(2,3), B(8,9) Step 3: x-coordinate: x = (2×8 + 1×2)/(2+1) = (16+2)/3 = 18/3 = 6 Step 4

Answer

Use when: Finding coordinates of a point dividing a line segment in a given ratio Formula: P(x,y) = [(m₁x₂ + m₂x₁)/(m₁+m₂), (m₁y₂ + m₂y₁)/(m₁+m₂)] Where: m₁:m₂ is the division ratio, (x₁,y₁) and (x₂,y

Answer

Step 1: Apply midpoint formula (special case of section formula with ratio 1:1) Midpoint = [(x₁+x₂)/2, (y₁+y₂)/2] Step 2: Substitute A(-3,5) and B(7,-1) Midpoint = [(-3+7)/2, (5+(-1))/2] Step 3: Simpl

Answer

Step 1: Let ratio be k:1. Use section formula P(1,4) = [(k×7 + 1×(-2))/(k+1), (k×10 + 1×1)/(k+1)] Step 2: From x-coordinate: 1 = (7k-2)/(k+1) Step 3: Cross multiply: 1(k+1) = 7k-2 k+1 = 7k-2 3 = 6k k

Answer

Step 1: Find distances AB, BC, and AC AB = √[(2-1)² + (3-5)²] = √[1+4] = √5 BC = √[(-2-2)² + (-11-3)²] = √[16+196] = √212 = 2√53 AC = √[(-2-1)² + (-11-5)²] = √[9+256] = √265 Step 2: Check if AB + BC =

Answer

Step 1: Point on y-axis has form P(0, y) Step 2: Set PA = PB (equidistant condition) √[(0-6)² + (y-5)²] = √[(0-(-4))² + (y-3)²] Step 3: Square both sides to eliminate square roots 36 + (y-5)² = 16 + (