Coordinate Geometry

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Using the formula: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)}| Step 1: Identify coordinates: (x₁,y₁)=(1,-1), (x₂,y₂)=(-4,6), (x₃,y₃)=(-3,-5) Step 2: Calculate first part: x₁y₂ + x₂y₃ + x…

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Method: Three points are collinear if the area of the triangle they form equals zero. Area = ½|{(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)}| Step 1: Coordinates: P(-1.5, 3), Q(6, -2), R(-3, 4) Ste…

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Formula: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)}| Step 1: Vertices in order: A(8,6), B(5,11), C(-5,12), D(-4,3) Step 2: First sum = (8)(11) + (5)(12) + (-5)(3) + (-4)(6)…

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Using: Area = ½|{(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)}| = 22 Step 1: Substitute values 22 = ½|{((-1)(-2) + (k)(4) + (7)(2)) - ((k)(2) + (7)(-2) + (-1)(4))}| Step 2: Simplify first part = 2 + …

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The slope m of a line passing through points A(x₁, y₁) and B(x₂, y₂) is: m = (y₂ - y₁)/(x₂ - x₁), where x₁ ≠ x₂ Alternatively, if θ is the angle of inclination with the positive x-axis: m = tan(θ) …

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Using slope formula: m = (y₂ - y₁)/(x₂ - x₁) Step 1: Identify coordinates: (x₁,y₁) = (-6,1) and (x₂,y₂) = (-3,2) Step 2: m = (2 - 1)/(-3 - (-6)) = 1/3 Answer: Slope = 1/3 Interpretation: - The slo…

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Context: Two non-vertical lines with slopes m₁ and m₂ are PERPENDICULAR if and only if m₁ × m₂ = -1 You use this condition when: - You need to verify if two lines are perpendicular - You need to find…

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Concept: Three points are collinear if slopes between consecutive pairs are equal. Step 1: Calculate slope of AB, where A(-2,5) and B(6,-1): m₁ = (-1 - 5)/(6 - (-2)) = -6/8 = -3/4 Step 2: Calculate …