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

Find the lengths of the medians of the triangle whose vertices are $(5, 6), (3, 8)$ and $(- 1, 2)$ .

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

17 units, 52 units, 17 units

17 units, 52 units, 11 units

17 units, 53 units, 17 units

19 units, 52 units, 17 units

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given vertices of a triangle are

5, 6, 3, 8, − 1, 2

From figure,
The medians AD, BE, and CF are drawn from vertices A, B, and C respectively.
So points D, E, and F are the midpoint of BC, AC, and AB respectively.
We know that,
If the coordinates of two points are

x 1, y 1

and

x 2, y 2

then the coordinate of the middle point of the two points will be

x 1 + x 2 2, y 1 + y 2 2

.
Then,
The co-ordinate of point D is

3 − 1 2, 8 + 2 2 = (1, 5)

.
The co-ordinate of point E is

5 − 1 2, 6 + 2 2 = (2, 4)

.
And,
The co-ordinate of point F is

5 + 3 2, 8 + 6 2 = (4, 7)

.
As the length of the median AD is the distance between point A and D, and we know that, the distance between any two points in a Cartesian plane

M a, b, N c, d

is given by

M N = (c − a) 2 + (d − b) 2

.
Then,

A D = (1 − 5) 2 + (5 − 6) 2 = 16 + 1 = 17

Similarly,

C F = (4 − (− 1)) 2 + (2 − 7) 2 = 25 + 25 = 50 = 52

And

B E = (2 − 3) 2 + (4 − 8) 2 = 1 + 16 = 17

Therefore, the length of the medians is

17 units, 52 units, 17 units

.
Hence, 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 Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!