Parallelism Math Example 4

Follow the full solution, then compare it with the other examples linked below.

hard

Parallelogram

PQRS

has

P(0,0)

Q(5,0)

R(7,4)

. Find coordinates of

S

so that

PQ \parallel SR

and

PS \parallel QR

1
Step 1: In a parallelogram, $\overrightarrow{PQ} = \overrightarrow{SR}$ . So $S = R - \overrightarrow{PQ} = (7,4) - (5,0) = (2,4)$ .
2
Step 2: Verify: $\overrightarrow{PS} = (2,4)$ and $\overrightarrow{QR} = (7-5, 4-0) = (2,4)$ . Equal vectors confirm $PS \parallel QR$ . ✓

Answer

S(2, 4)

Opposite sides of a parallelogram are parallel and congruent, so they share the same direction vector. Setting

\overrightarrow{SR} = \overrightarrow{PQ}

uniquely determines

S

About Parallelism

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