Q. 8 A4.8( 4 Votes )

# The coordinates of the middle points of the sides of a triangle are (1,1), (2,3) and (4,1), find the coordinates of its vertices. Consider a ΔABC with A(x1, y1), B(x2, y2) and C(x3, y3). If P(1, 1), Q(2, 3) and R(4, 1) are the midpoints of AB, BC, and CA. Then, …(i) …(ii) …(iii) …(iv) …(v) …(vi)

Adding (i), (iii) and (v), we get

x1 + x2 + x2 + x3 + x1 + x3 = 2 + 4 + 8

2(x1 + x2 + x3) = 14

x1 + x2 + x3 = 7 …(vii)

From (i) and (vii), we get

x3 = 7 – 2 = 5

From (iii) and (vii), we get

x1 = 7 – 4 = 3

From (v) and (vii), we get

x2 = 7 – 8 = -1

Now adding (ii), (iv) and (vi), we get

y1 + y2 + y2 + y3 + y1 + y3 = 2 + 6 + 2

2(y1 + y2 + y3) = 10

y1 + y2 + y3 = 5 …(viii)

From (ii) and (viii), we get

y3 = 5 – 2 = 3

From (iv) and (vii), we get

y1 = 5 – 6 = -1

From (vi) and (vii), we get

y2 = 5 – 2 = 3

Hence, the vertices of ΔABC are A(3, -1), B(-1, 3) and C(5, 3)

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  Smart Revision | Become a Master in Coordinate Geometry54 mins  Measuring distance by Distance formula49 mins  Champ Quiz | Previous Year NTSE Questions29 mins  Champ Quiz | Distance Formula30 mins  Set of Questions on Section Formula54 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 