Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
893 views
in Geometry and Algebra by (30.5k points)
closed by

The coordinates of the vertices of a quadrilateral, taken in order, are (2, 1), (5, 3), (8, 7), (4, 9).

i. Find the coordinates of the midpoints of all four sides.

ii. Prove that the quadrilateral got by joining these midpoints is a parallelogram.

1 Answer

+1 vote
by (30.8k points)
selected by
 
Best answer

i. Mid point of AB

\((\frac{2+5}{2},\frac{1+3}{2})\)

\((\frac{7}{2},\frac{4}{2})=(\frac{7}{2},2)\)

= P(3,5,2)

= S(3,5)

ii. Length of PQ

Length of QR

Length of RS = \(\sqrt{(6-3)^2+(8-5)^2}\)

\(=\sqrt{3^2+3^3}=\sqrt{18}\)

Length of PS = \(\sqrt{(3.5-3)^2+(2-5)^2}\)

\(=\sqrt{5^2+3^2}=\sqrt{9.25}\)

PQ = RS

RQ = PS

Since the opposite sides of the quadrilateral PQRS are equal it is a parallelogram.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...