Saved Bookmarks
| 1. |
Show that points p(2,-2) Q(7,3) R(11,-1) and s(6,-6) are vertices of a parallelogramp(2,-2) Q(7,3) R(11,-1) and s(6,-6) are the vertices of a parallelogram |
|
Answer» Answer: Step-by-step explanation: P(2,-2),Q(7,3), R(11,-1) and S(6,-6) By distance formula , PQ=(7−2)2+[3−(−2)]2−−−−−−−−−−−−−−−−−−√ ∴=52+52−−−−−−√ ∴PQ=25+25−−−−−−√ ∴PQ=50−−√ ∴PQ=5×5×2−−−−−−−−√ ∴PQ52–√...(1) QR=(11−7)2+(−1−3)2−−−−−−−−−−−−−−−−−−√ ∴QR=42+(−4)2−−−−−−−−−−√ ∴QR=16+16−−−−−−√ ∴QR=32−−√ ∴QR=2×2×2×2×2×−−−−−−−−−−−−−−−−√ ∴QR=42–√ ...(2) RS=6−11−−−−−√2+[−6−(−1)]2) ∴RS=−5−−−√2+(−5)2) ∴RS=25+25−−−−−−√ ∴RS=50−−√ ∴RS=5×5×2−−−−−−−−√ ∴RS=52–√ ...(3) PS=(6−2)2+[−6−(−2)]2−−−−−−−−−−−−−−−−−−−−−√ ∴PS=42+(−4)2−−−−−−−−−−√ ∴16+16−−−−−−√ ∴PS=32−−√ ∴PS=2×2×2×2×2−−−−−−−−−−−−−−√ ∴PS2×2×2–√ ∴PS=42–√ ....(4) In □ PQRS PQ=RS ...[From (1) and (3)] QR=PS ...[From (2) and (4)] A quadrilateral is a PARALLELOGRAM , if both the pairs of its opposite sides are congruent ∴□ PQRS is parallelogram. ∴P,Q,R and S are vertices of a parallelogram |
|