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

In the $xy$ -coordinate plane, the coordinates of three vertices of a rectangle are $(1, 5)$ , $(5, 2)$ and $(5, 5)$ . What are the coordinates of the fourth vertex of the rectangle?

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

(1, 3)

(2, 2)

(3, 2)

(1, 2)

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

Given that, the intersection point of diagonals of the rectangle is the midpoint of each diagonal,

(1, 5)

(5, 2)

and

(5, 5)

are the three coordinates.
Let the fourth coordinate be

(x, y)

.
Midpoint of two point

{(x}_{1}, y_{1})

{(x}_{2}, y_{2})

is ,

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

.
Midpoint of diagonal one is between points

(1, 5)

and

(5, 2)

.
Midpoint =

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

……..(1)
Midpoint of diagonal two is between points

(x, y)

and

(5, 5)

.
Midpoint =

(\frac{x + 5}{2}, \frac{y + 5}{2})

……….(2)
Equating x coordinates of equation (1) and (2),

\frac{x + 5}{2} = \frac{1 + 5}{2}

\Rightarrow x + 5 = 1 + 5

\Rightarrow x = 6 - 5

\Rightarrow x = 1

And, also equating y coordinates of equation (1) and (2),

\frac{y + 5}{2} = \frac{2 + 5}{2}

\Rightarrow y + 5 = 7

\Rightarrow y = 7 - 5

\Rightarrow y = 2

So, the coordinate

(x, y)

(1, 2)

.
Therefore, option (1) is correct.

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!