Question

22. Find out the co-ordinates of the points which divides internally the line joining the point \( (2,1) \) and \( (6,7) \) in the ratio( \( 3: 2) \). What will be the co-ordinate if it is divided externally?

Ask by Collins Ruiz. in Nepal
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The point divides the line segment internally at \( (4.4, 4.6) \) and externally at \( (14, 19) \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To find the coordinates of the point that divides the line segment joining \( (2, 1) \) and \( (6, 7) \) in the ratio \( 3:2 \) internally, you can use the section formula. The formula for the coordinates \( (x, y) \) of the dividing point is given by: \[ x = \frac{m x_2 + n x_1}{m + n} \quad \text{and} \quad y = \frac{m y_2 + n y_1}{m + n} \] where \( m \) and \( n \) are the parts of the ratio and \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the points. Here, \( (x_1, y_1) = (2, 1) \), \( (x_2, y_2) = (6, 7) \), \( m = 3 \), and \( n = 2 \). Calculating: \[ x = \frac{3 \cdot 6 + 2 \cdot 2}{3 + 2} = \frac{18 + 4}{5} = \frac{22}{5} = 4.4 \] \[ y = \frac{3 \cdot 7 + 2 \cdot 1}{3 + 2} = \frac{21 + 2}{5} = \frac{23}{5} = 4.6 \] So, the internal division gives the point \( \left(4.4, 4.6\right) \). For the external division in the ratio \( 3:2 \), you use the same formula, but with a negative sign for the ratio's second term: \[ x = \frac{m x_2 - n x_1}{m - n} \quad \text{and} \quad y = \frac{m y_2 - n y_1}{m - n} \] Calculating: \[ x = \frac{3 \cdot 6 - 2 \cdot 2}{3 - 2} = \frac{18 - 4}{1} = 14 \] \[ y = \frac{3 \cdot 7 - 2 \cdot 1}{3 - 2} = \frac{21 - 2}{1} = 19 \] Thus, the external division gives the point \( \left(14, 19\right) \).

Latest Geometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy