Math Problem Statement
ABCD is a parallelogram. AB = 3√ 2, AD = 8, ∠BAD = 45◦ , M is a point on CD, CM : MD = 1 : 2. N is a point on AD, AN : ND = 3 : 1. Find: a) the length of AM; b) the length of BN;
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Parallelograms
Section Formula
Distance Formula
Formulas
Section formula: P(x, y) = [(m * x2 + n * x1) / (m + n), (m * y2 + n * y1) / (m + n)]
Distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2]
Theorems
Properties of Parallelograms
Pythagorean Theorem
Section Formula
Suitable Grade Level
Grades 9-12
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