Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

What is the fourth vertex D of a parallelogram ABCD whose three vertices are $A (− 2, 3), B (6, 7)$ and $C (8, 3)$ ?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(0, - 1)

(1, 2)

(2, 5)

(0, - 3)

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given that the three vertices of a parallelogram ABCD are

A (− 2, 3), B (6, 7)

and

C (8, 3)

.
We know that the parallelogram's diagonals bisect each other, and the midpoint of the coordinates of both diagonals is equal.
Let, the fourth unknown vertex be (x, y).
Let us draw the figure.
Question Image

By the property of the parallelogram, the midpoint of AC = the midpoint of BD.
The midpoint formula is given by

P (x, y) = (\frac{x_{2} + x_{1}}{2}, \frac{y_{2} + y_{1}}{2})

By placing the values in the above relation, we get the below value.

(− 2 + 8 2, 3 + 3 2) = (6 + x 2, 7 + y 2)

On simplifying the above expression, we get -

(3, 3) = (6 + x 2, 7 + y 2)

On comparing the respective co-ordinates, we get the value of x and y as,

3 = 6 + x 2, 3 = 7 + y 2

⇒ x = 0

and

y = (− 1)

Hence,

(x, y) = (0, − 1)

Since, we get the fourth coordinate

(x, y) = (0, − 1)

.
Hence, the correct option is 1.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!