Multiply by 2-digit numbers: complete the missing steps

Learning Objectives Accurately calculate the square of a 2-digit radius (r²) to write the standard equation of a circle. Identify and fill in missing partial products in the standard algorithm for 2-digit multiplication. Apply the distance formula by correctly squaring 2-digit differences in x and y coordinates. Use 2-digit multiplication to find the constant term needed when completing the square for a circle's general equation. Verify the components of a circle's equation by deconstructing and completing multiplication steps. Distinguish between the radius (r) and the radius squared (r²) in circle equations, avoiding common calculation errors. Ever wondered how GPS pinpoints your location within a circular range? It all comes down to precise calculations! 🗺️ In...

TermDefinitionExample Standard Equation of a CircleThe formula (x - h)² + (y - k)² = r², which defines a circle with a center at point (h, k) and a radius of length r.The equation (x - 3)² + (y + 1)² = 25 represents a circle with its center at (3, -1) and a radius of 5. Radius Squared (r²)The value that completes the circle equation, found by multiplying the radius (r) by itself. This value represents the square of the distance from the center to any point on the circle.If a circle has a radius r = 12, then the radius squared is r² = 12 x 12 = 144. Distance FormulaA formula derived from the Pythagorean theorem used to find the distance between two points (x₁, y₁) and (x₂, y₂) in the coordinate plane.The distance between (1, 2) and (4, 6) is √((4-1)² + (6-2)²) = √(3² + 4²) = √25 = 5. Stand...

Standard Equation of a Circle (x - h)² + (y - k)² = r² This formula defines a circle with center (h, k) and radius r. Calculating r² when r is a 2-digit number is a key application of the skill in this lesson. Distance Formula (Squared Form) d² = (x₂ - x₁)² + (y₂ - y₁)² Used to find the square of the distance between two points. This is useful for finding the radius squared (r²) if you know the center and a point on the circle. The terms (x₂ - x₁)² and (y₂ - y₁)² may involve squaring 2-digit numbers. Completing the Square Term For x² + bx, add (b/2)² To complete the square for an expression like x² + bx, you must add the term (b/2)². If b is a large even number, b/2 can be a 2-digit number that you need to square.