Maths · Distance formula, sections formula, locus and its equation
is a parallelogram. is a point on which divides in the ratio intersects at is a
\( A B C D \) is a parallelogram. \( L \) is a point on \( B C \) which divides \( B C \) in the ratio \( \mathbf{1}: \mathbf{2} . \boldsymbol{A} \boldsymbol{L} \) intersects \( \boldsymbol{B} \boldsymbol{D} \) at \( \boldsymbol{P} . \boldsymbol{M} \) is a point on \( D C \) which divides \( D C \) in the ratio 1: 2 and \( A M \) intersects \( B D \) in \( Q \) Point \( P \) divides \( A L \) in the ratio
- A. 1: 2
- B. 1: 3
- C. 3: 1
- D. 2: 1
Step-by-step solution
Assign coordinates: A(0,0), B(3,0), C(3,3), D(0,3). L divides BC in ratio 1:2, so L(3,1). AL: y=(1/3)x, BD: x+y=3. Intersection P(9/4,3/4). Since A(0,0) and L(3,1), P = (3/4)L, so AP:PL = 3:1.
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