Q. 3 D4.0( 4 Votes )

# A (1,4) and B (4,8) are two points. P is a point on AB such that AP = AB + BP. If AP = 10 find the coordinates of P.

Given: AP = AB + BP and AP = 10

Firstly, we find the distance between A and B

d(A,B) = √(x2 – x1)2 + (y2 – y1)2

= √(4 – 1)2 + (8 – 4)2

= √(3)2 + (4)2

= √9 + 16

= √25

= 5

So, AB = 5

It is given that AP = AB + BP

10 = 5 + BP

10 – 5 = BP

BP = 5

A, B and P are collinear

and since AB = BP

B is the midpoint of AP

Let the coordinates of P = (x,y)

x + 1 = 8 and y + 4 = 16

x = 7 and y = 12

Hence, the coordinates of P are (7, 12)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Some Interesting Proofs in Geometry36 mins
Section Formula30 mins
Previous Year RMO Questions43 mins
NCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in Triangles33 mins
Champ Quiz | Distance Formula30 mins
Set of Questions on Section Formula54 mins
Measuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE QuestionsFREE Class
Coordinate Geometry Important Questions38 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses